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Explore a groundbreaking lecture on constructing quantum gravity duals from conformal field theory (CFT) operator algebras. Delve into a comprehensive recipe that combines conformal bootstrap, topological symmetries, tensor networks, and innovative renormalization techniques. Examine how quantum 2D Liouville theory exemplifies the construction of gravitational path integrals using "BCFT Legos" - local pieces of boundary conformal field theory correlations. Uncover the explicit connections between geometric data, algebraic structures, and quantum entanglement in this illuminating talk that brings the "It from Qubit" concept to life.