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: SLMath: Eisenbud Auditorium

Tags/Keywords

harmonic analysis
Hausdorff dimension
Besicovitch sets
Kakeya conjecture

Primary Mathematics Subject Classification

00B20 - Proceedings of conferences of general interest
11N32 - Primes represented by polynomials; other multiplicative structures of polynomial values
26A15 - Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable {For properties determined by Fourier coefficients, see 42A16; for those determined by approximation properties, see 41A25, 41A27}
14R99 - None of the above, but in this section

Secondary Mathematics Subject Classification No Secondary AMS MSC

Video

Zahl

Abstract

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

Supplements

	Zahl Notes 162 KB application/pdf	Download

Video/Audio Files

Zahl

H.264 Video	15-Zahl.mp4 563 MB video/mp4 rtsp://videos.msri.org/Zahl/15-Zahl.mp4	Download

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