  We present a line of research aimed at investigating holographic dualities in
the context of three dimensional quantum gravity within finite bounded regions.
The bulk quantum geometrodynamics is provided by the Ponzano-Regge state-sum
model, which defines 3d quantum gravity as a discrete topological quantum field
theory (TQFT). This formulation provides an explicit and detailed definition of
the quantum boundary states, which allows a rich correspondence between quantum
boundary conditions and boundary theories, thereby leading to holographic
dualities between 3d quantum gravity and 2d statistical models as used in
condensed matter. After presenting the general framework, we focus on the
concrete example of the coherent twisted torus boundary, which allows for a
direct comparison with other approaches to 3d/2d holography at asymptotic
infinity. We conclude with the most interesting questions to pursue in this
framework.
