Diff. Geom, Math. Phys., PDE Seminar: Jérôme Bertrand

In this talk, I will discuss some analytical aspects in the study of a finite dimensional Alexandrov space. Loosely speaking, the question I will consider is: to what extent does an Alexandrov space resemble a Riemannian manifold? In the first part of the talk, I will recall the background of Alexandrov's theory of metric spaces with curvature bounded from below, including results on the topology of these spaces.