This lecture is the fourth part of a mini-course exploring the solvability of Schramm-Loewner Evolution (SLE) through its connections with Liouville Quantum Gravity (LQG). Delve into the fascinating relationship between SLE—a random planar curve that emerges as the scaling limit of interfaces in critical statistical physics models like percolation and the Ising model—and its remarkable role in describing interfaces in conformal welding of LQG surfaces. Throughout this 59-minute presentation from the Hausdorff Center for Mathematics, examine the intricate interplay between SLE, LQG, and conformal field theory (CFT), discover exact identities connecting SLE to CFTs with central charge c < 1, and learn how a three-point correlation function of SLE corresponds with the imaginary DOZZ formula from CFT.