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Analysis Seminar

Thursday, April 4, 2024 - 3:30pm

Eyvindur Palsson

Virginia Tech


University of Pennsylvania

DRL 4E19

The Falconer distance problem, a continuous analogue of the celebrated Erdos distance problem asks: How large does the Hausdorff dimension of a Borel set, in the plane or higher dimensions, need to be to ensure that the Lebesgue measure of its distance set is positive? This question has seen much progress in recent years, yet the conjectured threshold remains open. After a quick introduction of this problem I will give an overview of a number of variants leading to a formulation of a restricted Falconer distance problem with a particular example being a diagonally restricted distance set.