# Meeting Details

Title: Fourier dimension and its modifications Center for Dynamics and Geometry Colloquium Joerg Schmeling, Lund University Fourier dimension has proved to be a useful tool to estimate Hausdorff dimensions of subsets of $\mathbb{R}^n$. It is also used in metric number theory and harmonic analysis. However it is not really justified to call it a dimension. We will investigate stability of the Fourier dimension under unions of sets and give positive results as well as counterexamples. As an outcome of these studies we will propose a modification of the Fourier dimension. This modification regularizes this notion in several ways. First it behaves like a dimension. It also has an important counterpart for measures. In particular we can show that the set of Borel measures having a given Fourier dimension is determined by its joint zero sets.