This paper explores the connection between three-dimensional quantum gravity with a negative cosmological constant and Virasoro conformal field theory (CFT). The authors develop a formalism for computing the gravity partition function using Virasoro TQFT, which is compared to the semiclassical evaluation of Euclidean gravity partition functions. This comparison leads to the refined volume conjecture, which relates the partition function to the volume of hyperbolic three-manifolds. The paper also discusses the structural properties of Virasoro TQFT, including the volume conjecture, the volume of hyperbolic tetrahedra, and the consistency conditions on the crossing kernels. The authors then apply the formalism to holographic examples, focusing on multi-boundary wormholes and their relation to the structure constants in the proposed ensemble dual. They also investigate the figure eight knot complement as a hyperbolic three-manifold, showing that the Virasoro TQFT partition function matches that of Teichmüller TQFT. The paper concludes with a discussion of the implications of these results for the holographic correspondence and the consistency of the Virasoro TQFT framework.This paper explores the connection between three-dimensional quantum gravity with a negative cosmological constant and Virasoro conformal field theory (CFT). The authors develop a formalism for computing the gravity partition function using Virasoro TQFT, which is compared to the semiclassical evaluation of Euclidean gravity partition functions. This comparison leads to the refined volume conjecture, which relates the partition function to the volume of hyperbolic three-manifolds. The paper also discusses the structural properties of Virasoro TQFT, including the volume conjecture, the volume of hyperbolic tetrahedra, and the consistency conditions on the crossing kernels. The authors then apply the formalism to holographic examples, focusing on multi-boundary wormholes and their relation to the structure constants in the proposed ensemble dual. They also investigate the figure eight knot complement as a hyperbolic three-manifold, showing that the Virasoro TQFT partition function matches that of Teichmüller TQFT. The paper concludes with a discussion of the implications of these results for the holographic correspondence and the consistency of the Virasoro TQFT framework.