Given a simple Lie algebra \mathfrak{g}, a positive integer l and an n-tuple of dominant integral weights for \mathfrak{g} at level l, one can define a vector bundle on M_g,n\bar known as a vector bundle of conformal blocks. These bundles are nef in the case that genus is zero and so this family provides potentially an infinite number of elements in Nef(M_0,n\bar) to analyze.

 It is an open question as to whether the nef cone, Nef(M_0,n\bar), is finitely generated for n > 7. It is natural to ask how this infinite family of conformal blocks divisors lives in Nef(M_0,n\bar). Is the subcone generated by conformal blocks divisors polyhedral? In this talk, we give several results to these questions for specific cases of interest. To show our results, we use a correspondence of the ranks of these bundles with quantum cohomology of the Grassmannian.