
Speaker: 
Claire Debord, U. Blaise Pascal, ClermontFerrand

Title: 
Groupoids and pseudodifferential calculus I

Abstract: 
The aim is to understand the pseudodifferential calculus on a smooth
groupoid as a convolution on a bigger groupoid. We will express order
zero pseudodifferential operators on \(G\) as integrals of kernels
associated with the adiabatic deformation \(G_{ad}\) of \(G\). We will
then use this fact in order to construct an explicit Morita
equivalence between the \(C^*\)algebra of order \(0\) pseudodifferential
operators on \(G\) and (an ideal of) the \(C^*\)algebra of the groupoid
\(G_{ga}\) obtained as the crossed product of \(G_{ad}\) by the natural
\(\mathbb{R}_+^*\) action it carries.

