Hairer’s Reconstruction Theorem and multi-level Schauder estimates without regularity structures.

Martin Hairer’s regularity structures are a recent discovery and, despite their spectacular applications, they are still relatively little known in the mathematical community. Recently, in joint work with F. Caravenna and L. Broux/F. Caravenna we have revisited the main analytical tools of this theory with the aim of making these notions both more general and simpler to understand. The aim of this talk is to present the main ideas of this construction.