For many types of random planar maps, i.e. planar graphs embedded in the sphere, it is known that their geometry possesses a scaling limit described by a universal random continuous metric space known as the Brownian sphere. I will give a short overview of its properties and its relation to Liouville Quantum Gravity and discuss ways to escape the universality class by introducing matter degrees of freedom or vertices with heavy-tailed degree distribution. The peeling process will be introduced as a general method to explore planar maps, and can be used to study the geometry of models in the Brownian sphere universality class and beyond.

Date

Dec 7, 2018

Event

Location

Utrecht, The Netherlands

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