This theory project aims at identifying mechanisms for exerting spatial and time-dependent control of quantum material properties in order to engineer and design desirable quantum states and dynamical phenomena. We are examining the use of twist-engineering and electrostatic control of moiré heterostructures of 2d materials to create clean and tunable analog realizations of correlated quantum phenomena such as non-Fermi liquids, heavy fermion criticality, and topological phases, in ways that take advantage of the large superlattice structure and narrow bandwidth to achieve spatial control on the microscopic moiré superlattice scales. We are also investigating how to narrow electronic bandwidths can be exploited to achieve coherent time-dependent driving without excessive heating, in order to create novel dynamical phases of matter.