Multiplicity of critical points of master functions and Schubert   calculus
  In [MV], some correspondences were defined between critical points of master functions associated to sl_{N+1} and subspaces of C[x] with given ramification properties. In this paper we show that these correspondences are in fact scheme theoretic isomorphisms of appropriate schemes. This gives relations between multiplicities of critical point loci of the relevant master functions and multiplicities in Schubert calculus. 
Prakash Belkale, Evgeny Mukhin, Alexander Varchenko