  Schubert calculus has been in the intersection of several fast developing
areas of mathematics for a long time. Originally invented as the description of
the cohomology of homogeneous spaces it has to be redesigned when applied to
other generalized cohomology theories such as the equivariant, the quantum
cohomology, K-theory, and cobordism. All this cohomology theories are different
deformations of the ordinary cohomology. In this note we show that there is in
some sense the universal deformation of Schubert calculus which produces the
above mentioned by specialization of the appropriate parameters. We build on
the work of Lerche Vafa and Warner. The main conjecture there was that the
classical cohomology of a hermitian symmetric homogeneous manifold is a Jacobi
ring of an appropriate potential. We extend this conjecture and provide a
simple proof. Namely we show that the cohomology of the hermitian symmetric
space is a Jacobi ring of a certain potential and the equivariant and the
quantum cohomology and K-theory is a Jacobi ring of a particular deformation of
this potential. This suggests to study the most general deformations of the
Frobenius algebra of cohomology of these manifolds by considering the versal
deformation of the appropriate potential. The structure of the Jacobi ring of
such potential is a subject of well developed singularity theory. This gives a
potentially new way to look at the classical, the equivariant, the quantum and
other flavors of Schubert calculus.
