On the big quantum cohomology of coadjoint varieties

Quantum cohomology of homogeneous spaces $G/P$ is a rich mathematical object that has received considerable attention in the past decades. In this talk we'll present a proof of the generic semisimplicity of the big quantum cohomology for the so called coadjoint homogeneous spaces in all Dynkin types and its relations to the singularity theory. If time permits, we'll discuss related phenomena in the derived categories of coherent sheaves. The talk is based on a joint work with Nicolas Perrin.