PIRSA:13100110

The Stokes groupoids

APA

Gualtieri, M. (2013). The Stokes groupoids. Perimeter Institute. https://pirsa.org/13100110

MLA

Gualtieri, Marco. The Stokes groupoids. Perimeter Institute, Oct. 23, 2013, https://pirsa.org/13100110

BibTex

          @misc{ pirsa_13100110,
            doi = {},
            url = {https://pirsa.org/13100110},
            author = {Gualtieri, Marco},
            keywords = {},
            language = {en},
            title = {The Stokes groupoids},
            publisher = {Perimeter Institute},
            year = {2013},
            month = {oct},
            note = {PIRSA:13100110 see, \url{https://pirsa.org}}
          }
          

Abstract

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 field theory. 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 differential 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.