Abstract. I will discuss a new holographic duality between a 1d theory, the q-Schwarzian, and certain 2d dilaton gravity theories. This q-Schwarzian is a one parameter deformation of the well known Schwarzian theory. For real values of q, upon quantization, the q-Schwarzian mechanics exactly reproduces DSSYK amplitudes. For values of q on the unit circle, it exactly reproduces Liouville gravity amplitudes. The gravity duals are respectively dilaton gravity with a sine, and a sinh potential. The former is independently interesting because it has cosmological features. The duality can be derived via the first order formulation of the gravity models as topological gauge theories. More low-brow, one can match the classical solutions, I will focus on this. I will also highlight peculiar features related to the difference between temperature and ”tomperature” in the DSSYK version of the duality.