  A theorem of Dubrovin establishes the relationship between the GUE partition
function and the partition function of Gromov-Witten invariants of the complex
projective line. Based on this theorem we derive loop equations for the
Gaussian Unitary Ensemble (GUE) partition function. We show that the GUE
partition function is equal to part of the topological partition function of
the non-linear Schr\"odinger (NLS) Frobenius manifold.
