In recent years, various formulations of the Uncertainty Principle have found applications in the study of PDEs like unique continuation or observability/controllability properties of solutions. There are also some instances where properties of solutions of PDEs find applications to the Uncertainty Principle.

The aim of this talk is to present some of those interactions based on several joint works (K. Beauchard, A. Fernández-Bertolin, K. Gröchenig, K. Kellay, V. Komornik, Y. Lyubarskii, , E. Malinnikova, K.-M. Perfekt, K. Pravda-Starov)