Analysis & Applications Seminar
A construction of Kakeya Sets in Arbitrary Dimension
Speaker: Rafael J. Fernández-Delgado (ICMAT-UAM)Date: Friday, 25 September 2026 - 11:30Place: Aula 520, Módulo 17, Departamento de Matemáticas, UAM
Abstract:
We construct Kakeya sets in arbitrary dimension d ≥ 2, generalizing the classical Perron tree construction beyond dimension 2. The Kakeya sets we construct have δ-neighbourhood of volume at most C| log δ|−(d−1), which improves on previously known constructions, and which is conjecturally optimal. We further derive consequences for the Lp-boundedness of radial Fourier multipliers in terms of Besov spaces with logarithmic smoothness.
