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Distance set problem and weighted Fourier extension estimates

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Speaker: E. Burak Erdogan, UC Berkeley
Location: 693 Kerr
Start time: Thu, Feb 19 2004, 4:10PM

Falconer's distance set conjecture states that if a compact subset $E$ of $\mathbb{R}^d$ ($d>1$) has Hausdorff dimension greater than $d/2$ then its distance set, $D(E):=\{|x-y|:x,y\in E\}$, has positive Lebesgue measure. In this lecture, we will discuss the recent progress in this conjecture and closely related Fourier extension estimates relative to fractal measures.