On the descriptive complexity of Fourier dimension and Salem sets

Abstract: It is known that, for Borel sets, the Fourier dimension is less than or equal to the Hausdorff dimension. The sets for which the two notions agree are called Salem sets.

In this talk, we explore the descriptive complexity of the family of closed Salem subsets of the Euclidean space. We also show how these results yield a characterization of the Weihrauch degree of the maps computing the Hausdorff or the Fourier dimensions.

logic

Audience: researchers in the topic

Computability theory and applications

Series comments: Description: Computability theory, logic

The goal of this endeavor is to run a seminar on the platform Zoom on a weekly basis, perhaps with alternating time slots each of which covers at least three out of four of Europe, North America, Asia, and New Zealand/Australia. While the meetings are always scheduled for Tuesdays, the timezone varies, so please refer to the calendar on the website for details about individual seminars.