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This lecture is the first part of a mini-course exploring the solvability of Schramm-Loewner Evolution (SLE) through its connection to Liouville Quantum Gravity (LQG). Discover how SLE emerges as the scaling limit of interfaces in critical statistical physics models like percolation and the Ising model, while also serving as the interface in conformal welding of LQG surfaces. Examine the fascinating interplay between SLE, LQG, and conformal field theory (CFT), including derivations of exact identities connecting SLE to CFTs with central charge c < 1. Learn how a three-point correlation function of SLE corresponds to the imaginary DOZZ formula from CFT. Presented by Morris Ang at the Hausdorff Center for Mathematics, this one-hour lecture provides deep mathematical insights into these interconnected theoretical frameworks.
