|Date:||Fri, April 28, 2017|
|Place:||Lecture Hall, Research I|
Abstract: This talk is about various aspects of the Fourier dimension and its variants. Fourier dimension gives a link between harmonic analysis, geometric measure theory, potential theory, dynamics and related concepts. One aspect of the talk is to relate, and contrast the Fourier dimension with the Hausdorff dimension. Moreover we will present some questions where the Fourier rather than the Hausdorff dimension can be successfully applied. This includes uniform distribution problems and questions from geometric measure theory like the occurrence of (dynamical) Salem sets. There have been several similar but different notions of the Fourier dimension subject to different applications. We will argue that these various notions are indeed different and also do not behave like a regular dimension-like quantity. We also will give an alternative more regular definition, both in the sense of a dimension-like characteristic as well as a well-behaved functional analytic quantity. This modification still reflects most of the important properties that are needed for applications.
The colloquium is preceded by tea from 11:45 in the Resnikoff Mathematics Common Room, Research I, 127.