A pseudo-differential calculus for singular filtrations of the tangent bundle and index theorem

Mercredi 16 juin 16:00-18:00 - Omar Mohsen - Münster

Résumé : Starting from Folland and Stein’s work, people have defined inhomogeneous principal symbols for differential operators in various generalisations. The goal of this symbol is to prove that operators like Hormander’s sum of squares are hypoelliptic. In this talk I will define an inhomogeneous principal symbol associated to a singular filtration of the tangent bundle (a filtration by locally finitely generated submodules of the module of vector fields). I will then define an associated deformation groupoid and a pseudo-differential calculus. In the end I will show how the inhomogeneous principal symbol computes the index of differential operators which are elliptic in such calculus (equivalently any maximally hypoelliptic differential operator)
This is joint work with Androulidakis, van-Erp, Yuncken.

Lieu : Demander le lien Zoom à jean-michel.bismut@universite-paris-saclay.fr

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