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*Closed geodesics on surfaces.*

## Résumé

This talk will be about closed geodesics on hyperbolic surfaces and some of their properties. In particular, the following questions will be discussed:

- Given an integer n > 0, among all closed geodesics with at least n self-intersection points,there is at least one of shortest length. How many self-intersection points doessuch a geodesic have?

- Simple closed geodesics are nowhere dense on a surface, so to ”fill” a surface you need self-intersection points. How many?

Based on oint work with Viveka Erlandsson and with Ara Basmajian and Juan Souto