Speaker
Bart Zonneveld
(Radboud University)
Description
The moduli space of hyperbolic surfaces (roughly the set of all unique hyperbolic surfaces) is an interesting object in random geometry and its properties also have applications in a quantum gravity toy-model called JT gravity. There exists a topological recursion by Mirzakhani which allows us to compute the total volumes of these moduli spaces, but this formulation gives us little insight in the different contributing surfaces.
In this talk I will discuss another formulation that allows us to describe the moduli space (at least for genus 0) using trees with simple additional data. This tree bijection reproduces the same total volumes as Mirzakhani’s recursion, but also opens the possibility to look at more complicated statistics.
