Date/heure
26 février 2025
10:45 - 12:00
Lieu
Salle de conférences Nancy
Oratrice ou orateur
Teo Gil Moreno de Mora i Sardà ( Université Paris-Est Créteil and the Universitat Autònoma de Barcelona)
Catégorie d'évènement
Séminaire des doctorants
Résumé
A fundamental question in geometry consists in understanding the effect of curvature on the shape of geometric spaces. In the case of surfaces, the Gauss-Bonnet Theorem establishes a link between the curvature of a surface and its topology. For example, it allows us to understand the topology of surfaces whose curvature is positive at every point.
When considering higher-dimensional geometric objects, called manifolds, we can define different notions of curvature. Scalar curvature is the weakest of these notions, and for this reason it is difficult to extract topological or geometric information from it. In particular, can we describe the topology of a manifold with positive scalar curvature?
In this talk, I will explain why this is an interesting question, and I will present a classification result for 3-dimensional manifolds with positive scalar curvature. This is a collaborative work with F. Balacheff and S. Sabourau.