Nina Holden is an Associate Professor at the Courant Institute of Mathematical Sciences at New York University. She completed her PhD in 2018 at MIT under the supervision of Scott Sheffield and was then a postdoc at ETH Zurich. Her research is in probability theory and mathematical physics and she is particularly interested in two-dimensional random geometry and conformally invariant random objects. She is associate editor of the Annals of Probability and Annales de l’Institut Henri Poincare and has received recognitions such as the Maryam Mirzakhani New Frontiers Prize and the Rollo Davidson prize.
This 2024 Schramm lecture will be delivered at the 11th World Congress in Probability and Statistics in Bochum, Germany, August 12–16, 2024: https://www.bernoulli-ims-worldcongress2024.org

Scaling limits of random planar maps

Planar maps are graphs embedded in the sphere such that no two edges cross, where we view two planar maps as equivalent if we can get one from the other via a continuous deformation of the sphere. Planar maps are studied in many different branches of mathematics and physics. In particular, in probability theory and theoretical physics random planar maps are used as natural models for discrete random surfaces.
An active research direction within probability theory in the past two decades has been to establish scaling limit results for planar maps. It has been proven that random planar maps converge in various senses or topologies to continuum random surfaces called Liouville quantum gravity (LQG) surfaces. The latter surfaces are highly fractal and have their origin in string theory and conformal field theory. In this talk we will present convergence results for planar maps and we will focus in particular on a notion of convergence known as convergence under conformal embedding.