Ordinary differential equations become much less ordinary
when they are allowed to have singularities.
Solving them naively in formal power series, one often obtains divergent
series, just as in the perturbation series for physical observables in quantum
The asymptotic interpretation of this divergent series
exhibits the famous Stokes phenomenon, an essential ingredient in any full
description of the solutions to the system. I will explain a new viewpoint on singular ODE which
illuminates the geometric meaning of the phenomena described above, and which
can be applied to the problem of resummation of formal power series.
This viewpoint uses a very basic but underused tool in
geometry: Lie groupoids. A Lie groupoid is as natural and essential an object as a Lie group; I
shall explain how to build examples of them and how to use them to solve
singular differential equations.