Joint IAS/PU Arithmetic Geometry

The notion of singular support has its origin in the theory of partial differential equations, and was introduced to the world of constructible sheaves by M. Kashiwara and P. Schapira in the 1970s. It is a basic invariant (like the support), and, together with the characteristic cycle, has applications in many areas, including partial differential equations, geometric Langlands, and exponential sums. In this talk, I will discuss the singular support in three contexts: complex analytic spaces (Kashiwara and Schapira), algebraic varieties (A. Beilinson, T. Saito), and rigid analytic varieties (in progress).