The microlocal theory of constructible sheaves

The microlocal point of view says that the study of an object on a manifold benefits from systematic constructions involving the cotangent bundle. It was introduced by M. Sato in the 1960s in the field of partial differential equations, and has since spread to many other fields. In this talk, I will first introduce the basic ingredients of the microlocal theory of sheaves on manifolds as developed by M. Kashiwara and P. Schapira, then I will discuss recent developments and open questions in the analogous theories in the positive characteristic algebraic context and the non-Archimedean analytic context.