Mathematics Colloquia and Seminars

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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.