Uncertainty relations and applications in spectral and control theory

This is an extended abstract for the Oberwolfach Workshop 2101b \emph{Geometry, Dynamics and Spectrum of Operators on Discrete Spaces} organized by David Damanik, Matthias Keller, Tatiana Smirnova-Nagnibeda, and Felix Pogorzelski. It took place in online format from 3rd to 9th January 2021.