A quantum mechanical particle subject to a periodic potential possesses allowed energy regions (energy bands) separated by forbidden energy regions (band gaps). In some cases the energy interval corresponding to a band can shrink down to a single value and the band becomes flat. This means that the particle can not move and it is said to be localized. Motion in a flat band is enabled by interparticle interactions which allow the particles to move in pairs. The correlated motion of these so-called Cooper pairs is at the origin of superconductivity and it has been predicted that flat bands can dramatically enhance the critical temperature of the superconducting transition, even above room temperature. Disorder promotes localization and tends to destroy superconductivity. Since disorder is always present in solids, the goal of this project is to understand the effect of disorder on a superconductor living in a flat band.