The interface between the two band insulators SrTiO3 and LaAlO3 has the unexpected properties of a two-dimensional electron gas. It is even superconducting with a transition temperature, T(c), that can be tuned using gate bias V(g), which controls the number of electrons added or removed from the interface. The gate bias-temperature (V(g), T) phase diagram is characterized by a dome-shaped region where superconductivity occurs, that is, T(c) has a non-monotonic dependence on V(g), similar to many unconventional superconductors. Here, we report, the frequency of the quantum resistance-oscillations versus inverse magnetic field for various V(g). This frequency follows the same non-monotonic behaviour as T(c); a similar trend is seen in the low field limit of the Hall coefficient. We theoretically show that electronic correlations result in a non-monotonic population of the mobile band, which can account for the experimental behaviour of the normal transport properties and the superconducting dome.