Speaker
Description
Two-dimensional quantum gravity models fall in three classes: Liouville gravity, for which the geometry is wildly random in the bulk; topological gravity, for which the geometries, having constant curvature and geodesic boundaries, have a finite number of moduli; and an intermediate class of models, which has attracted a lot of attention recently, for which the metrics have constant curvature but the boundaries can fluctuate wildly. These so-called Jackiw-Teitelboim models have been studied in the physics literature, mainly for negative curvature, under poorly understood assumptions and in a certain limit for which the boundary length goes to infinity.
The aim of the talk will be to present a first-principle approach to JT gravity without assuming that a particular limit is taken, mainly focusing on the disk topology. Because the curvature is fixed, the randomness entirely comes from the fluctuating disk boundary, which is a closed curve immersed in the hyperbolic space, the plane or the sphere. The goal is thus to count closed curves that bound a disk, a very interesting and non-trivial combinatorial problem. Our construction, which relies on good old conformal gauge techniques and insights from recent developments, yields a new class of random geometrical models with many properties that remain to be explored.
