Derived deformations and quantum cohomology

The simplest example of the interpretation of quantum cohomology as a deformation phenomenon is
served by the comparison of (genus zero) quantum cohomology ring of $P^n$ with miniversal unfolding space of the singularity
$A_n$. I will be discussing the vast generalization of the deformation formalism and speculating about its possible
applications to quantum cohomology theory.