Laura Monk

Counting non-simple geodesics on random hyperbolic surfaces

In her breakthrough article of 2013, Mirzakhani provided a method to sample random hyperbolic surfaces and study their geometric properties. She obtained bounds on various geometric quantities, such as the length of their systole and their diameter. Her techniques rely on computing averages of certain functions which can be expressed in terms of multicurves, i.e. families of simple disjoint curves. The hypothesis that the curves are simple and disjoint is crucial to these techniques, and a strong limitation to applications to other problems. In my recent works with Nalini Anantharaman, we provide a variety of tools and new results allowing to count non-simple geodesics on random hyperbolic surfaces.