A classical question in geometric measure theory, introduced by
Falconer in the 80s is, how large does the Hausdorff dimension of a
compact subset in Euclidean space need to be to ensure that the
Lebesgue measure of its set of pairwise Euclidean distances is
positive. In this talk, I will report some recent progress on this
problem, which combines several ingredients including Orponen's
radial projection theorem, and the refined decoupling theory.
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Last modified: April 11 2016 - 18:14:43