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SUMMARY:Kevin Ren (Princeton)
DTSTART:20230919T180000Z
DTEND:20230919T190000Z
DTSTAMP:20260423T004132Z
UID:OARS/49
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/OARS/49/">Sh
 arp Furstenberg sets estimate in the plane</a>\nby Kevin Ren (Princeton) a
 s part of OARS Online Analysis Research Seminar\n\n\nAbstract\nFix two rea
 l numbers $s \\in (0\, 1]$\, $t \\in (0\, 2]$. A set $E \\subset \\mathbb{
 R}^2$ is a $(s\, t)$-Furstenberg set if there exists a set of lines $\\mat
 hcal{L}$ with Hausdorff dimension $t$ such that for each line $\\ell \\in 
 \\mathcal{L}$\, we have $\\dim_H (E \\cap \\ell) \\ge s$. (For example\, a
  Kakeya set in $\\mathbb{R}^2$ is a special case of a $(1\, 1)$-Furstenber
 g set.) The Furstenberg sets problem asks for the minimum possible Hausdor
 ff dimension of a $(s\, t)$-Furstenberg set for any given pair of $s\, t$.
  In this talk\, I will illustrate the rich theory linking this problem to 
 the discretized sum-product problem\, orthogonal projections\, and the hig
 h-low method in Fourier analysis. Joint works with Yuqiu Fu and Hong Wang.
 \n
LOCATION:https://researchseminars.org/talk/OARS/49/
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