Tuesday 13 October 2026, 16:00 - 17:00 in HG00.065
Timothy Budd (Radboud)
Random planar geometry seen from the boundary
After an introduction to random (planar) maps and their role in two-dimensional quantum gravity, I'll explain how the combinatorics of planar maps (with the topology of the disk) is linked to the theory of orthogonal polynomials and how this link provides a handle on geodesic distances between points on the boundary circle. An analogous combinatorial story around chord diagrams on the circle received considerable attention in the physics literature recently in the context of holography and the DSSYK model. These phenomena turn out to be closely related by what one might, informally, think of as an example of "holography in combinatorics": chord diagrams capture precisely the geodesic boundary metric of (bipartite) planar maps and, for special choices of weights, the map model on the disk induces precisely to the chord diagram model on the boundary circle. If time permits, I'll comment on connections to an analogous story in hyperbolic geometry.