Abstract: In recent years, there has been remarkable progress in evaluating wormhole amplitudes in 3d Einstein gravity with negative cosmological constant and matching them to statistics of 2d CFT data. In the talk, I will first give an overview of how wormholes in 3d gravity capture the universal matrix element statistics of local operators in 2d CFT and of certain extended operators dual to dust shells in 3d gravity, which provides a realization of ETH consistent with Virasoro symmetry in 3d gravity. I will also describe how wormholes constructed from domain walls help provide a precision test for this realization of ETH. I will then describe a framework – Fragmentation of knots and links by Wilson lines – that can systematically compute Gaussian and non-Gaussian contributions to these statistics. I will illustrate this idea by constructing multi-boundary wormholes from fragmentation diagrams of prime knots and links – including hyperbolic ones like the figure-eight knot and the Whitehead link; and non-hyperbolic ones like the Hopf link and the trefoil knot. Using Virasoro TQFT, I will show how the partition functions on wormholes constructed from different fragmentations of the same knot or link are closely related. Finally, I will comment on how fragmented knots contribute to the sum over geometries in 3d gravity due to their relation to rational tangles.