In this talk, I will present JT gravity and the Virasoro string, models of two-dimensional quantum gravity on constant negatively curved spacetimes and as two coupled CFTs, respectively, as models of random surfaces. This common mathematical framework provides a unique lens to explore the similarities and differences between these models within the moduli space of Riemann surfaces. A detailed exploration of their mathematical aspects, particularly focusing on their generating functions, facilitates a seamless integration of tools from each model. This integration not only enhances our understanding of each model individually but also provides insights into coupling these theories with defects or branes and exploring critical regimes where the surfaces develop macroscopic holes.
