Jean-Marie Lescure, Université Blaise Pascal de Clermont-Ferrand:   Groupoids and index theory for singular spaces.

 
We will see how the non commutative tangent space of manifold with conical singularities can be used to produce analytical and topological index maps similar to those defined by M. Atiyah and I. Singer on a smooth manifold. In the conical case, we will briefly explain how the analytical index map is related to Fredholm index of suitable elliptic operators. We will show how the framework of groupoids unify the smooth and conical cases. Then, we will present partial advances in the generalization of the previous ideas for general stratified spaces.