## [18] Reconstructing SLE-decorated Liouville quantum gravity surfaces from random permutons (with Ewain Gwynne).

Permutons constructed from a Liouville quantum gravity surface and a pair of space-filling Schramm-Loewner evolutions (SLEs) have been shown — or are conjectured — to describe the scaling limit of various natural models of random constrained permutations. We prove that, in two distinct and natural settings, these permutons uniquely determine, modulo rotation, scaling, translation and …