| Résume | On one hand, the Topological Recursion (TR) of Chekhov-Eynard-Orantin was interpreted by Kontsevich-Soibelman, and later on by Borot-Bouchard-Chidambaram-Creutzig-Noschenko, as computing partition functions of quantum Airy structures, especially so in the context of vacuum vectors of W-algebra representations. On the other hand, TR reconstructs solutions of differential systems from singular perturbation. Such differential systems however have to obey the Topological Type property in order for this to be the case, and for which sufficient conditions have been discovered over the last decade. In this talk, we will discuss the extension of the underlying circle of ideas for wild rational differential systems of (r,s) type. The tame case of logarithmic systems is simpler, and by now pretty well understood. This is part of a joint work with Bouchard, Krammer, and Nelsen, the rest of which concerns deformations, and might be mentioned if time allows. |
