6 ψ$_{Q}$ = det( Z ) $^{Q}$ψ$_{0}$ (1) The simplest wave functions which do this are powers of determinants of one of the complex matrices Z (these are wave functions describing many giant gravitons on top of each other, at weak coupling they are described by similar formulae involving operators of the full matrices [32, 33]. At strong coupling, the giant gravitons condense into a topology change once the gravitational backreaction is taken into account). The matrix Z is a diagonal matrix. The eigenvalues represent one of the three complex coordinates determining R 6 ≃ C 3 as a complex manifold. Such wave functions are of the form where Z + X 1 + iX 2 for example, and Q is an arbitrary integer. When N is finite, the system (with the wave function) should be considered as a version of quantum geometry at finite values of ℏ . The quantity 1 /N plays such a role in the AdS geometry. After all N 1 / 4 measures the size of AdS in Planck units. Thus, finite N effects and how fluctuations depend on N can be said to encode quantum gravity corrections. The idea of this paper is to gain some understanding of emergent quantum geometry. Since we do not have direct access to the ten dimensional geometry from current methods, we will use the quenched field theory geometry to explore the problem of convergence to large N and the problem of determining the shape of the geometry at finite N . A similar problem has been studied in [34, 35] for the case of fuzzy geometries of brane embeddings (where the brane configurations are non-abelian). In our case the notion of shape needs to be refined with respect to the thermodynamic limit. What we call geometry according to the prescription [5, 18] is characterized by the (support of the) large N density of eigenvalue distributions, properly rescaled by the size of the ground state, √$_{N}$$_{. This can be shown to}$ be a singular distribution of R 6 in the thermodynamic limit, namely the eigenvalues form a manifold of lower dimension, for some general class of BPS wave functions [5, 23]. However, this is just the saddle point description at large N of the wave function. This procedure does not take into account that the eigenvalues are discrete, or that there are fluctuations around this saddle point. At finite N we expect that there are corrections to this geometric saddle point approx- imation of the wave function. These quantum corrections will be due both to granularity of the constituents (the system has finitely many eigenvalues in R $^{6}$), as well as due to the quantum spread of the wave function (so that the support of the wave function is not sin-