Geometry of random planar maps and genus-0 hyperbolic surfaces


In this mini-course I will explain how some of the combinatorial techniques used in the study of random planar maps, i.e. embedded graphs in the sphere, have natural analogues for genus-0 hyperbolic surfaces with boundaries. In particular, this opens up the opportunity to study statistical properties of geodesic distances in hyperbolic surfaces with many boundaries or cusps sampled from the Weil-Petersson measure.

University of Montreal, Canada