Title: On the descriptive complexity of Fourier dimension and Salem sets
by Manlio Valenti (Università di Udine) as part of Computability theory and applications
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.