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- The Stokes groupoids

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.

Event Type:

Seminar

Collection/Series:

Speaker(s):

Event Date:

Wednesday, October 23, 2013 - 14:00 to 15:30

Location:

Lazaridis Theatre

©2012 Perimeter Institute for Theoretical Physics