Lecture notes on Gaussian multiplicative chaos and Liouville Quantum Gravity

Understand

The purpose of these notes, based on a course given by the second author at Les Houches summer school, is to explain the probabilistic construction of Polyakov's Liouville quantum gravity using the theory of Gaussian multiplicative chaos.

• In particular, these notes contain a detailed description of the so-called Liouville measures of the theory and their conjectured relation to the scaling limit of large planar maps properly embedded in the sphere.
• These notes are rather short and require no prior knowledge on the topic.