Outer automorphisms of free groups are studied via their action on Culler Vogtmann Outer Space. The program presented in the talk involves understanding the space of geodesics in Outer Space and how they can be used to better understand the outer automorphism group of the free group.

This is joint work with Yael Algom-Kfir, Ilya Kapovich, Joseph Maher, Lee Mosher, and Sam Taylor.