MATJ5122 MA3: Random Geometry and Embeddability (JSS34) (2 op)

This course aims to convey the basic structure of two important objects in random geometry: the Brownian continuum random tree and the Brownian map. We will take several approaches to defining the objects and study their local (metric) properties. To do this we will also delve into dimension theory and consider embeddability and their repercussions.

The lecture course will be (mostly) self-contained and no specific background in random geometry or dimension theory is assumed. There will be several exercises throughout the week and pass/fail will be based on successful completion of the exercises.

After this mini-course, the participants are expected to be familiar with the definitions and basic properties of the Brownian continuum random tree, the Brownian map, as well as their relations to other objects in random geometry. Participants will be able to use methodology from probability, dynamical systems, and geometric analysis to analyse local and global scaling behaviour of these objects.

Undergraduate level probability, real analysis and properties of metric spaces, basic point set topology will also be helpful.