Applications of the Multisummability theory in Complex Analysis

The theory of multisummability for solutions of complex differential equations with an isolated singularity is an important achievements in Dynamics of the 20's theory. In a certain sense, it is a theory of how to describe solutions of such differential equations in a "large" sector with the vertex at the singularity, and how then to uniquely recognize a solution by its Taylor series (at the singularity). In this talk, we show unexpected applications of the multisummability theory for classification problems for real submanifolds in complex space.