Classification of G-structures by integrating Lie algebroids
The aim of this talk is to explain a very fruitful approach to the classification of manifolds with a geometric structure (Riemannian, complex, Kähler etc.) subject to a PDE. I will introduce the language of G-structures, its connection to coframes, and will talk about (Élie) Cartan's realization and equivalence problems: when can a set of functions be realized as the structure functions of a coframe? When are two realizations (locally) isomorphic? Locally this was already more or less solved by Cartan.
In suitable cases (i.e. under the right regularity) this turns out to be closely related to the integration problem of Lie algebroids to Lie groupoids. This allows us to find and classify global solutions. I will illuminate the story with as many examples as time permits.
