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SUMMARY:Turning a Needle: An Analyst’s Perspective
DTSTART:20260504T083000Z
DTEND:20260504T092500Z
DTSTAMP:20260509T115100Z
UID:indico-event-16494@indico.math.cnrs.fr
DESCRIPTION:Speakers: Rafael José Fernández-Delgado Ruiz\n\nKakeya’s n
 eedle problem asks what is the smallest area in which a unit line segment 
 can be continuously rotated inside a planar set. Despite its elementary fo
 rmulation\, the problem leads to highly counterintuitive constructions and
  plays a central role in modern analysis.In this talk\, we give a brief in
 troduction to Kakeya and Besicovitch sets\, starting from the historical d
 evelopment of the needle problem and Besicovitch’s construction of measu
 re-zero sets containing a unit segment in every direction. We then introdu
 ce fractal dimensions as a way to quantify the size of these sets\, leadin
 g to Kakeya’s conjecture and its current status.We conclude by highlight
 ing some applications of Kakeya-type constructions in harmonic analysis an
 d their connections to major open problems.\n\nhttps://indico.math.cnrs.fr
 /event/16494/
LOCATION:Fokko du Cloux (ICJ)
URL:https://indico.math.cnrs.fr/event/16494/
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