The phase retrieval problem

In applications, it is often impossible to measure the phase of a signal, and one must recover it from some additional physical "redundancy" present in the problem. Phase retrieval problems arise in diverse fields, ranging from crystallography to quantum mechanics. Mathematically, the analysis of the problem unites many fields, including functional analysis, harmonic analysis, PDE, AI, probability, and more. I will discuss recent advances on this topic in a way suitable for a general audience.