The microlocal codimension three conjecture

Abstract:

According to an old well-established principle special functions (or distributions)  can be understood and analyzed in terms of the systems of differential equations they satisfy. To this end, a general theory of systems of linear (micro) differential equations was developed by the Sato school.  This point of view,  in its various incarnations, is now ubiquitous in many parts of mathematics. For example,  in the geometric Langlands program and representation theory it allows  us to replace functions and group representations  by geometric objects. We will discuss the main longstanding conjecture, the codimension three conjecture, concerning the general structure of holonomic systems and indicate the outline of its proof.  This is joint work with Masaki Kashiwara.