In this talk, we will discuss recent progress in understanding quantum gravity amplitudes in Liouville and JT gravity.
We focus on two main results: the Liouville gravity results can be viewed as q-deformations of the JT answers, and Liouville gravity can be written as a 2d dilaton gravity model with a sinh dilaton potential.
These facts can be linked when using the Poisson-sigma model framework.
We end with some prospects towards understanding generic dilaton gravity models. Based on arXiv:2109.07770 and earlier work.
