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Speaker: Georges Skandalis, U. Paris VII
Title: Groupoids and pseudodifferential calculus II
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.
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