We have recently demonstrated the significant influence that interactions between cavity quantum electromagnetic fields and topological quantum materials—such as quantum Hall systems and 2D moiré materials—can have on their quantum transport and topological properties. In this theoretical internship, the Master's student will gain expertise in and apply advanced theoretical techniques from quantum many-body physics and cavity Quantum Electrodynamics (QED). This internship, which may lead to a subsequent PhD, will focus on exploring non-trivial topological phases in fractional quantum Hall systems and fractional Chern insulators. These are crucial strongly correlated quantum materials for both fundamental physics and applications in topological quantum information.