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An improved bound on the Hausdorff dimension of Besicovitch sets in R^3

Recent Developments in Harmonic Analysis May 15, 2017 - May 19, 2017

May 19, 2017 (11:00 AM PDT - 12:00 PM PDT)
Speaker(s): Joshua Zahl (University of British Columbia)
Location: MSRI: Simons Auditorium
  • harmonic analysis

  • Hausdorff dimension

  • Besicovitch sets

  • Kakeya conjecture

Primary Mathematics Subject Classification
Secondary Mathematics Subject Classification No Secondary AMS MSC



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

28695?type=thumb Zahl Notes 162 KB application/pdf Download
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