Closed geodesics on surfaces and Riemannian manifolds

Geodesics are special paths in surfaces and so-called Riemannian manifolds which connect close points in the shortest way. Closed geodesics are geodesics which go back to where they started. In this snapshot we talk about these special paths, and the efforts to find closed geodesics.
Snapshots of modern mathematics from Oberwolfach;2017,05