2D Percolation, Random Triangulation, and Liouville Quantum Gravity

Explore the fascinating world of 2D random geometry in this 50-minute lecture by Xin Sun at BIMSA. Delve into the fundamental meta-conjecture connecting Liouville quantum gravity (LQG) to the scaling limit of discrete random surfaces under conformal embedding. Gain insights into the motivation behind studying LQG and its mathematical construction. Learn about the groundbreaking proof by Nina Holden and Xin Sun, which confirms the meta-conjecture for uniformly sampled triangulations using the Cardy-Smirnov embedding. Discover the link between this discrete conformal embedding and Smirnov's proof of Cardy's formula for 2D percolation, bridging the gap between discrete and continuous models in random geometry.