On the spectrum of the Dirac operator on degenerating Riemannian surfaces

Date/heure
4 avril 2024
14:15 - 15:15

Lieu
Salle de séminaires Metz

Oratrice ou orateur
Cipriana Anghel-Stan (Göttingen)

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


Résumé

We study the behaviour of the spectrum of the spin Dirac operator on degenerating families of Riemannian surfaces, when the length of a simple closed geodesic shrinks to zero. We work under the hypothesis that the spin structure along the pinched geodesic is non-trivial. It is well-known that the spectrum of an elliptic differential operator on a compact manifold varies continuously under smooth perturbations of the metric. The difficulty of our problem arises from the non-compactness of the limit surface, which is of finite area with two cusps.