Closed geodesics on surfaces.




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