Recent experimental studies on twisted bilayer graphene (TBG) and other twisted materials have revealed unexpectedly complex phase diagrams with exotic phases of quantum matter. Among them, they revealed highly unconventional superconducting phases with ultra-flat bands, which cannot be described by the conventional BCS theory. Due to their very low Fermi velocity, the superconducting coherence length xi, predicted by BCS theory (which is proportional to the Fermi velocity) is more than 20 times shorter than the measured values. Recent theoretical developments show that the coherence length is instead governed by the quantum metric of the Bloch states. When a magnetic impurity is embedded in a superconductor, its local moment acts as a Cooper pair breaker, creating intra-gap bound state excitations whose spatial extent can be extremely large and is governed by xi. In this internship, we would like to analyze the problem of a magnetic impurity in a flat-band superconductor and decipher if and how the quantum metric shows up in the bound state equations. In the longer term, our understanding of hybrid systems involving such flat-band superconductors needs to be completely revised: this includes all the quantum engineering that has been developed with mesoscopic superconductors.