Formulating string theory or M-theory by a gauge theory is an attractive idea which has been extensively studied. Especially, realisation of geometries from the lower dimensional gauge theory is an intriguing and challenging problem. The necessity of such emergent geometry suggests that there should be a phase transition in the gauge theory and that a geometry would appear as its temperature decreases. In this talk, we focus on the BMN matrix model, which is considered as a non-perturbative formulation of M-theory on the pp-wave geometry and also conjectured to have a gauge/gravity duality, which relates the vacua on the gauge theory side to bubbling geometries in the type IIA supergravity. Our preliminary results of Monte Carlo simulations show two phase transitions and one of them looks related with emergent geometry