Patrik Wahlberg: Singularities of functions and distributions

We give a survey of how to measure singularities of functions and distributions. Singularities mean a lack of smoothness of a given type. Since 50 years it has been known that many phenomena in PDEs become clearer when singularities are described in phase space, that is, a dual variable is introduced which describes the directions of the singularities. This leads to Hörmander's concept of wave front set. We will discuss different kinds of wave front sets, including global ones, which capture smoothness and decay at infinity comprehensively.