Carleson meets Calderón

I will present a surprising connection between the inverse problem which consists of determining a potential from the scattering amplitude at fixed energy and Carlesson problem of convergence to initial data of the time dependent non elliptic Schrödinger equation. As a byproduct we show that potential with half derivative square integrable can be recovered from the scattering amplitude and that the method fails below that regularity. This is a joint work with Kari Astala from Helsinki and Keith M Rogers from Madrid.