The Microlocal codimension three conjecture
by Professor Kari Vilonen
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 that they satisfy. To this end, a general theory of systems of linear (micro) differential equations was developed by the Sato school in Kyoto. This point of view, in its various incarnations, is now ubiquitous in many parts of mathematics allowing functions to be replaced by geometric objects. In joint work with Kashiwara we have proved the main longstanding conjecture in this subject, the codimension three conjecture. I will explain this conjecture and some of the very general ideas which enter the proof.