Séminaires : Séminaire d'Analyse et Géométrie

Equipe(s) :
Responsables :O. Biquard, A. Deruelle, E. Di Nezza, I. Itenberg, X. Ma
Email des responsables : {olivier.biquard, alix.deruelle, eleonora.dinezza, ilia.itenberg, xiaonan.ma}@imj-prg.fr
Salle : 15–25.502
Adresse :Jussieu

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Orateur(s) Michal Wrochna - Cergy Paris Université,
Titre An index theorem on asymptotically static spacetimes with compact Cauchy surface
Horaire15:45 à 17:00
RésumeA theorem due to Bär and Strohmaier (Amer. J. Math., 141 (5)) says that the Dirac operator on a Lorentzian manifold with compact Cauchy surface is Fredholm if Atiyah-Patodi-Singer boundary conditions are imposed at finite times. Furthermore, the index is given by a geometric formula that parallels as closely as possible the Atiyah-Patodi-Singer theorem in the Riemannian setting. In this talk I will report on joint work with Dawei Shen (Sorbonne Université) which extends this result to the infinite-time setting. Furthermore, we prove that in the infinite time situation, Fredholm inverses are Feynman parametrices in the sense of Duistermaat-Hörmander, a property which allows to show relationships with local aspects of the geometry.