Séminaire de Mathématiques Accessibles

Sara AZZALI (Université de Postdam) : " Introduction to index theory"

Séminaire de Mathématiques Accessibles à l'Institut Camille Jordan :

Des exposés d'1 heure, au rythme d'un exposé par mois, accessibles à un public plus large que les séminaires spécialisés traditionnels.

Public visé :
- au moins tout enseignant chercheur en maths pures et appliquées.
- souvent enseignants chercheurs d'autres disciplines connexes, étudiants...
- ponctuellement, public plus large (lycéens...).

Orateur : Sara AZZALI (Université de Postdam)

Titre : "Introduction to index theory"

Résumé : The celebrated index theorem of Atiyah and Singer provides a fundamental link between an analytic object (the index of an elliptic operator) and the geometric and topological properties of the underlying compact manifold.  
This talk will give an overview of this classical result, some of its geometric applications, and sketch the proof relying on the "heat-kernel method”.
If time allows, we will introduce other important spectral invariants studied in index theory and discuss their geometrical and topological significance.  
In the talk, all the important concepts will be introduced at least by examples.

As prerequisite : it helps to have already met manifolds, to know some basic differential geometry and have notions of functional analysis such as Banach and Hilbert spaces.