Explore the intersection of 3D gravity and Teichmüller Topological Quantum Field Theory (TQFT) in this 48-minute conference talk by Lorenz Eberhardt from the Institute for Advanced Study. Delve into the classical story, mapping class groups, face space, and tight space concepts. Examine crossing transformations, the hexagon identity, and TQFT's precise relation to 3D gravity. Investigate wormholes, tetrahedrons, and manifolds, with a focus on singular cases. Gain insights into the foundations of holography and quantum gravity as part of the "Gravity from algebra: modern field theory methods for holography" conference at the Kavli Institute for Theoretical Physics.