The idea of compactifying the space of Riemannian manifolds satisfying Ricci curvature lower bounds goes back to Gromov in the '80ies and was pushed by Cheeger-Colding in the ‘90ies, who

The idea of compactifying the space of Riemannian manifolds satisfying Ricci curvature lower bounds goes back to Gromov in the '80ies and was pushed by Cheeger-Colding in the ‘90ies, who

The idea of compactifying the space of Riemannian manifolds satisfying Ricci curvature lower bounds goes back to Gromov in the '80ies and was pushed by Cheeger-Colding in the ‘90ies, who

The idea of compactifying the space of Riemannian manifolds satisfying Ricci curvature lower bounds goes back to Gromov in the '80ies and was pushed by Cheeger-Colding in the ‘90ies, who

The purpose of this course is to introduce the synthetic treatment of sectional curvature upper-bound on metric spaces. The basic idea of A.D. Alexandrov was to characterize the curvature bounds

The purpose of this course is to introduce the synthetic treatment of sectional curvature upper-bound on metric spaces. The basic idea of A.D. Alexandrov was to characterize the curvature bounds

The purpose of this course is to introduce the synthetic treatment of sectional curvature upper-bound on metric spaces. The basic idea of A.D. Alexandrov was to characterize the curvature bounds

The purpose of this course is to introduce the synthetic treatment of sectional curvature upper-bound on metric spaces. The basic idea of A.D. Alexandrov was to characterize the curvature bounds

We propose a class of local definitions of weak lower scalar curvature bounds that is well defined for C0 metrics. We show the following: that our definitions are stable under greater-than-second

In this talk, we shall describe some topological rigidity and its relationship with positive scalar curvature. Precisely, we will present a proof that a complete contractible 3-manifold with

This is a series of lectures on Bishop--Gromov's type inequalities adapted to metric spaces. We consider the case of Gromov-hyperbolic spaces and draw consequences of these inequalities such as

This is a series of lectures on Bishop--Gromov's type inequalities adapted to metric spaces. We consider the case of Gromov-hyperbolic spaces and draw consequences of these inequalities such as