Xin Sun 2D percolation random triangulation and Liouville quantum gravity ICBS2024

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A fundamental meta-conjecture in 2D random geometry is that Liouville quantum gravity (LQG) describes the scaling limit of certain natural discrete random surfaces under a conformal embedding. In this lecture I will explain the motivation for studying LQG, the mathematical construction of LQG, and a proof by Nina Holden and myself of the meta-conjecture in the case of uniformly sample triangulation, under a discrete version of the conformal embedding called the Cardy-Smirnov embedding. This embedding comes from Smirnov's proof of Cardy's formula for 2D 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