Abstract:

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 theories, mainly in negative curvature, have been intensively studied in the physics literature in recent years. They build a bridge between several different problems, from strongly coupled electron systems in condensed matter theory to quantum black hole models. They are analysed using a variety of techniques, including matrix models, Mirzakhani/Eynard recursion relations, integration over Diff(S1)/PSL(2,R), etc.