Finite cut-off holography and Matrix models

In this talk, I will discuss finite-cutoff models of two-dimensional topological gravity and their relation to random matrix theories. Random matrix models have emerged as a useful tool for understanding and refining semiclassical holographic dualities, particularly in low-dimensional quantum gravity. I will begin with a brief introduction to large-(N) matrix models and then describe their connection to low-dimensional topological quantum field theories. Along the way, I will highlight how introducing a finite cutoff can lead to significant modifications in the growth of the black-hole interior compared with the matrix-model description of pure JT gravity. Finally, I will discuss the relation between (TT-bar)-deformed Schwarzian theories and their gravitational bulk duals, emphasizing how these deformations provide an avenue for exploring finite-cutoff holography and possible departures from the standard JT-gravity picture.