View from 
Villa Mondragone
Speaker: Claire Debord, U. Blaise Pascal, Clermont-Ferrand
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.
logo INDAM  logo CNRS  G ruppo di  R icerca  E uropeo  F ranco-  I taliano in  GE ometria  N on  CO mmutativa
roupement de echerche uropéen ranco talien en ométrie on mmutative