Off-shell Partition Functions in 3d Gravity

I will discuss partition functions in three-dimensional quantum gravity with negative cosmological constant in canonical quantization. I will review the phase space and its quantization in detail, which leads to the computation of the gravity partition functions on 3d manifolds which do not support semiclassical saddles. It is often simpler to consider chiral gravity that only captures the left-movers, since ordinary gravity gives divergent answers. I finally explain a dual description in terms of topological recursion of a certain part of the partition function that is the uplift of the random matrix model for JT-gravity. Based on 2204.09789.