An overview on Lie pseudgroups and geometric structures
Francesco Cattafi
Würtzburg
https://sites.google.com/view/francescocattafi/
Date(s) : 22/01/2026 iCal
9h30 - 10h30
The space of (local) symmetries of a given geometric structure has the natural structure of a Lie (pseudo)group. Conversely, geometric structures admitting a local model can be described via the pseudogroup of symmetries of such local model.
The main goal of this talk is to provide several examples and give an intuitive understanding of the slogan above, which can be made precise at various levels of generality (depending on the definition of « geometric structure ») and using different tools/methods.
Moreover, I will sketch a new framework, which include previous formalisms (e.g. G-structures or Cartan geometries) and allows us to prove integrability theorems. In particular, I will provide intuition on the relevant objects which make this approach work, namely Lie groupoids endowed with a multiplicative « PDE-structure » and their principal actions. Poisson geometry will give us the guiding principles to understand those objects, which are directly inspired from, respectively, symplectic groupoids and principal Hamiltonian bundles.
This is based on a forthcoming book written jointly with Luca Accornero, Marius Crainic and María Amelia Salazar.
Emplacement
I2M Saint-Charles - Salle de séminaire
Catégories
