Séminaires : Séminaire Géométrie et Topologie

Ce séminaire s’adresse aux géomètres, topologues et dynamiciens au sens large. Il est rattaché aux équipes Analyse Algébrique et Analyse Complexe et Géométrie. Les exposés seront accessibles à une audience large, doctorants inclus. Il se tiendra à Jussieu, le jeudi à 11h, en salle 15-25 502. Le séminaire a l'agenda google suivante: https://calendar.google.com/calendar/b/0?cid=dDgzNTJoczNmdDhlMm5nb2IzMXJwaWpsdHNAZ3JvdXAuY2FsZW5kYXIuZ29vZ2xlLmNvbQ

Almost exactly five years ago, I gave a colloquium talk here in Paris on the discovery with Christian Blohmann and Marco Cezar Fernandes of a groupoid symmetry closely mirroring the Poisson brackets of the initial value constraints for the Einstein evolution equations in general relativity.

At that time, we introduced a notion of "hamiltonian Lie algebroid" which we intended to use to make a more concrete connection between the groupoid and the constraints.  Unfortunately, we still have not established that connection, but the theory of hamiltonian Lie algebroids has taken on a life of its own.

In the symplectic case, it led to a problem in symplectic topology which has now been solved.

In this talk, I will focus on the case of hamiltonian Lie algebroids over Poisson manifolds, in which ongoing work with Blohmann and Stefano Ronchi has led to new insights relation to suggestions made by Alejandro Cabrera about the relation between Lie algebroids, connections, and Poisson structures.