Abstract. Classically, inverse function theorems are in finite-dimensional spaces, or in Banach spaces. It is well known that this framework is insufficient in many important cases, for instance when one deals with PDEs instead of ODEs. In such cases, one needs an inverse function theorem in C^\infty, which is a Fréchet space. Such theorems are called "hard" inverse function theorems; the first one is due to John Nash, and the method was clarified and extended by Jurgen Moser. There have been many variants since then, but all rely on the Newton approximation scheme, where the quadratic convergence overcomes the loss of derivatives. In this talk, I will review the general framework and describe a new result due to Éric Séré, Jacques Fejoz and myself, which does not use the Newton method.

Ab 15:45 Uhr, Kaffee und Kuchen im Common Room.