Following the works of Alexandrov, Mironov and Morozov, we show that the
symplectic invariants of \cite{EOinvariants} built from a given spectral curve
satisfy a set of Virasoro constraints associated to each pole of the
differential form ydx and each zero of dx . We then show that they satisfy
the same constraints as the partition function of the Matrix M-theory defined
by Alexandrov, Mironov and Morozov. The duality between the different matrix
models of this theory is made clear as a special case of dualities between
symplectic invariants. Indeed, a symplectic invariant admits two decomposition:
as a product of Kontsevich integrals on the one hand, and as a product of 1
hermitian matrix integral on the other hand. These two decompositions can be
though of as Givental formulae for the KP tau functions.Comment: 19 page
