  This paper is devoted to the study of the quantum cohomology of coadjoint
varieties of simple algebraic groups across all Dynkin types. We determine the
non-semisimple factors of the small quantum cohomology ring and relate them to
ADE-singularities. Moreover, we show that the big quantum cohomology of a
coadjoint variety is always generically semisimple even though in most cases
the small quantum cohomology is not.
