Tuomas Sahlsten

Obstructions to localisation of functions in both position and momentum at fractals

We discuss about our recent work on Fourier coefficients of fractal distributions (self-similar, self-conformal, self-affine) and what kind of motivations they have had in localisation of functions at “small sets” (e.g. points or fractals) in both position (geometric side) and momentum (Fourier side). If time permits, we will review some connections to the Klein-Gordon equation by Hedenmalm and Montes-Rodríguez, and some uses in scattering theory by Bourgain, Dyatlov et al. Based on joint works with Jialun Li (Zürich) and Connor Stevens (Manchester).