Wendelin Werner: Conformal Loop Ensembles on Liouville Quantum Gravity (or how to construct a plane as a patchwork of disks).

I will describe an ongoing project with Jason Miller and Scott Sheffield. One of its goals it to show the special natural interplay in the continuous setting between Conformal Loop Ensembles (which are the natural conformally invariant collections of loops that one can define on a Riemann surface) and the Liouville Quantum Gravity surfaces (which are random equivalence classes of domains equipped with an area measure defined via the Gaussian Free Field). One shows for instance that the conformal loop ensembles can be obtained via conformal welding of an appropriately ordered infinite family of independent quantum surfaces.