Correlated topological phases in moire graphene systems

The nearly flat bands of many moire graphene systems are topological. The resulting interplay of band topology and strong correlations make these systems suitable platforms for many interesting phenomena, After reviewing the physics leading to orbital ferromagnetism and an associated quantum anomalous Hall effect in some of these systems. I will discuss theoretically the possibile reaiization of other correlated topological phases. Examples include fractional Chern insulators (possibly at zero external magnetic field), and interaction-driven time-reversal symmetric topological insulators. Time permitting I will also discuss the theoretical challenges and existing progress in describing strongly correlated systems in a partially full topological band.