### Random multi-geodesics on hyperbolic surfaces of large genus

Geometry and Topology Seminar

29th November 2022, 2:00 pm – 3:00 pm

Fry Building, 2.04

On a hyperbolic surface, a closed geodesic is said to be simple if it does not intersect itself, and a multi-geodesic is a disjoint union of simple closed geodesics. In this talk, I will explain how to pick a random multi-geodesic, and present an attempt to answer the following question: what is the shape of a random multi-geodesic on a hyperbolic surface of large genus? In particular, we will see that the average lengths of the first three largest connected components of a random multi-geodesic on a large genus hyperbolic surface is approximately,

75.8%, 17.1%, 4.9%, respectively, of the total length. This is joint work with Vincent Delecroix.

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