On unique continuation for the Schrödinger equation

Motivated by applications to approximate and exact controllability, we are interested in the following unique continuation question: assume the solution of the linear Schrödinger equation on a domain vanishes on a very small open set for a very short time interval, then is this solution identically zero? In the situation where the Schrödinger operator includes a potential, the answer to this question depends on the regularity of the latter. We present a result proved in [FLL24] which assumes that the potential is Gevrey <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mn>2</mml:mn> </mml:math> in time and bounded in space, relaxing in this context the analyticity assumption of the Tataru-Robbiano-Zuily-Hörmander theorem. We also give a sketch of proof.