Lecture
This lecture discusses the interplay between conformal field theory and Liouville quantum gravity, focusing on correlation functions and their solutions for surfaces with and without boundaries. The instructor presents two perspectives: the conformal field theory perspective, which emphasizes correlation functions and their solutions, and the random surface perspective, which describes quantum surfaces and their scaling limits. The lecture recaps theorems related to cutting Liouville quantum gravity (LQG) by Schramm-Loewner evolution (SLE) loops, highlighting the independence of resulting quantum surfaces. The instructor explains the significance of quantum annuli and pairs of pants, detailing their laws and relationships to boundary lengths. The discussion includes the solvability of loop lengths in LQG and the implications of these results for understanding quantum surfaces. The lecture concludes with computations involving SLE observables, demonstrating the application of these theoretical frameworks in practical scenarios.