Linear differential equations and Stokes structures

The formal study of linear differential equations is now well understood by means of Kedlaya-Mochizuki theorem. On the other hand, the analytic study of linear differential equations is still an active research topic, involving completely different techniques and structures. It can be carried out via at least three complementary points of view: the tannakian point of view (algebraic), the point of view of Stokes filtered local system (topological), and the point of view of Stokes torsors (geometric). The goal of this course is to explain how Stokes filtered local systems in dimension one classify local analytic differential equations of one variable. If time permits, we will give a survey on the tannakian and torsor aspects, as well as what is known in higher dimension.