|Location:||MSRI: Simons Auditorium|
A map is a gluing of polygons along their edges forming either the sphere or a torus with an arbitrary number of handles. These objects naturally appear in various domains such as mathematics, computer science and physics, and they have been the subject of many studies.
During this talk, we will adopt the point of view of scaling limits, consisting roughly in trying to see what a large random map looks like.
More precisely, we will address the problem of the convergence, as the size tends to infinity, of rescaled maps chosen uniformly at random in some privileged classes of maps with fixed size. We will see that a scaling limit exists for some specific classes of maps. This defines random metric spaces with interesting properties. We will in particular focus here on their topology. I will expose in this talk the main results of the field and try to give some of the principal ideas behind the study of these objects.