By Mingkun Liu
On a hyperbolic surface, a closed geodesic is said to be simple if it has no self-intersection. A multi-geodesic is a multiset of disjoint simple closed geodesics. A multi-geodesic can be decomposed into connected components, and therefore induces a partition of its total length. In this talk, I will present an attempt to answer the following question: what is the shape of the length partition of a random multi-geodesic on a hyperbolic surface with large genus? In particular, I will explain why the average lengths of the three largest components of a random multi-geodesic on a large genus hyperbolic surface are approximately, 75.8%, 17.1%, and 4.9%, respectively, of the total length. And we shall see that intersection numbers on the moduli spaces of curves have a crucial role to play. This is based on joint work with Vincent Delecroix.
By Alexander Soibelman
By Mingkun Liu
By Pierrick Bousseau
By Anna Barbieri
By Gabriele Rembado
By Pierrick Bousseau
By Joshua Lam
By Oscar Kivinen
By Elba Garcia-Failde
By Nezhla Aghaei
By Yves André
By Vasudevan Srinivas
