Conformal loop ensembles on Liouville quantum gravity 1

In these three lectures, I plan to describe our ongoing research program with Jason Miller and Scott Sheffield that deals with the natural interplay between Conformal Loop Ensembles and the Liouville Quantum gravity area measures. I will explain some features in the continuous world of CLE and LQG/GFF that do hopefully enlighten some of the basic features of the Quantum gravity approach to critical systems, and give a roadmap to understand the scaling limit of some decorated discrete planar maps models.