Last week, I gave a talk at IHES, where I presented my work on criticality in random hyperbolic surfaces. Hyperbolic surfaces appear in JT gravity, a model of quantum gravity in two dimensions. The phenomenon of criticality arises in the well-known O(N) loop model for random planar maps. In this regime, macroscopic loop configurations dominate the partition function. In JT gravity, this means that the coupling to certain kinds of branes makes 2D universes with very long geodesic boundaries proliferate. This is one of the many examples of how random geometry tools help us to find interesting phenomena in quantum gravity.

If you want to know more, the talk is available here: