Title: Rational curves of minimal degree on higher Fano manifolds (joint work with Carolina Araujo) Abstract: (Johan made this up so this is almost certainly not 100% accurate) We will discuss a notion of higher Fano variety introduced by de Jong/Starr (see for example ``Higher Fano manifolds and rational surfaces'' by these authors). We will especially study what one can say about the families of minimal degree rational curves that sweep out such a higher Fano variety. Related questions: Can one classify higher Fanos? Is there an inductive structure on the collection of all higher fano varieties?