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Dubrovin establishes the relationship between the GUE partition function andthe partition function of Gromov--Witten invariants of the complex projectiveline. In this paper, we give a direct proof of Dubrovin's result. We alsopresent in a diagram the recent progress on topological gravity and matrixgravity.

GUE via Frobenius Manifolds. I. From Matrix Gravity to Topological Gravity and Back