My specialty is theoretical condensed matter (solid-state) physics. My research has encompassed a wide variety of subfields, concentrating on disordered and/or strongly interacting (correlated) electronic materials in the past two decades. More recently, our emphasis has been in two areas – (i) magnetism and transport in in disordered electronic systems such as doped and diluted magnetic semiconductors, and (ii) two-dimensional electron systems (e.g. semiconductor heterostructures and graphene) in a strong magnetic field (the quantum Hall regime). Our research combines analytical methods, such as the concept of scaling, with numerical methods, such as Monte Carlo simulations, transfer matrix approach, and other matrix techniques to study fundamental properties of electronic materials . Recently, for example, we have studied (1) the nature of the magnetism in diluted magnetic semiconductors; (2) ground states of dopant clusters in quantum dots; and (3) properties of electronic eigenstates in disordered nanowires, to name a few. Calculations are carried out on high-performance multiprocessor computer arrays. Much of our research is motivated by, and closely related to, experimental systems. Currently we’re focusing our efforts on uncovering the design principles for fractional quantum Hall states, to determine the feasibility of topological quantum computing.