Pseudodifferential calculus using generalized fixed point algebras

Date/heure
6 octobre 2022
14:00 - 15:00

Lieu
Salle de séminaires Metz

Oratrice ou orateur
Eske Ewert (Hannover)

Catégorie d'évènement
Séminaire Théorie de Lie, Géométrie et Analyse

The principal symbol of a pseudodifferential operator is homogeneous and shows, therefore, a certain invariance under the ${\mathbb{R}}_{>0}$-action by scaling.The scaling action can be extended to the so called zoom action of ${\mathbb{R}}_{>0}$ on the tangent groupoid. In this talk, I will explain why order zero pseudodifferential operators can be viewed as generalized fixed points of the zoom action in the sense of Rieffel.
This method is applicable in more general situations, for example for filtered manifolds. Here, we recover the order zero pseudodifferential extension by van Erp and Yuncken. Our approach allows to compute the spectrum of the noncommutative symbol algebra. This gives a Fredholm criterion for pseudodifferential operators in this calculus in terms of a Rockland condition.