An improved bound on the Hausdorff dimension of Besicovitch sets in R^3
Recent Developments in Harmonic Analysis May 15, 2017 - May 19, 2017
Location: MSRI: Simons Auditorium
11K55 - Metric theory of other algorithms and expansions; measure and Hausdorff dimension [See also 11N99, 28Dxx]
28A75 - Length, area, volume, other geometric measure theory [See also 26B15, 49Q15]
A Besicovitch set is a compact set in R^d that contains a unit line segment pointing in every direction. The Kakeya conjecture asserts that every Besicovitch set in R^d must have Hausdorff dimension d. I will discuss a recent improvement on the Kakeya conjecture in three dimensions, which says that every Kakeya set in R^3 must have Hausdorff dimension at least 5/2 + \eps, where \eps is a small positive constant. This is joint work with Nets Katz
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