What is the most natural way of choosing a random surface (two-dimensional Riemannian
manifold)? If we are given a finite set 𝑋, the easiest way to choose a random element of 𝑋 is …

We endow the 8/3-Liouville quantum gravity sphere with a metric space structure and show
that the resulting metric measure space agrees in law with the Brownian map. Recall that a …

We study Liouville first passage percolation metrics associated to a Gaussian free field hh
mollified by the two-dimensional heat kernel pt p_t in the bulk, and related star-scale …

We survey the theory and applications of mating-of-trees bijections for random planar maps
and their continuum analog: the mating-of-trees theorem of Duplantier, Miller, and Sheffield …

The conformal bootstrap hypothesis is a powerful idea in theoretical physics which has led
to spectacular predictions in the context of critical phenomena. It postulates an explicit …

We consider an embedding of planar maps into an equilateral triangle $\Delta $ which we
call the Cardy embedding. The embedding is a discrete approximation of a conformal map …

Abstract For γ ∈ (0, 2) γ∈(0, 2), we define a weak γ γ-Liouville quantum gravity (LQG) metric
to be a function h ↦ D_h h↦ D h which takes in an instance of the planar Gaussian free field …

In 1987 Graeme Segal gave a functorial definition of Conformal Field Theory (CFT) that was
designed to capture the mathematical essence of the Conformal Bootstrap formalism …

We demonstrate that the conformal loop ensemble (CLE) has a rich integrable structure by
establishing exact formulas for two CLE observables. The first describes the joint moments …

We demonstrate how to obtain integrability results for the Schramm‐Loewner evolution
(SLE) from Liouville conformal field theory (LCFT) and the mating‐of‐trees framework for …