The peanosphere (or "mating of trees") construction of Duplantier, Miller, and Sheffield encodes certain types of $\gamma$-Liouville quantum gravity (LQG) surfaces ($\gamma \in (0,2)$) decorated with an independent ...

We establish existence and uniqueness for Gaussian free field flow lines started at interior points of a planar domain. We interpret these as rays of a random geometry with imaginary curvature and describe the way distinct ...