I am primarily interested in theories of strongly correlated quantum systems, particularly in low dimensions where quantum fluctuations can lead to interesting and exotic new states of matter. Examples of such systems include the fractional quantum Hall effect, in which a two-dimensional gas of electrons in a perpendicular magnetic field condenses into an incompressible quantum fluid whose elementary excitations exhibit fractional charge and statistics, and low-dimensional quantum antiferromagnets such as CsNiCl3, where quantum fluctuations at T = 0 rise to highly correlated ground states very different than the classical Neel state. Extensions of these models to include SU(N) spins (N > 2) or multicomponent quantum Hall systems open up additional possibilities, some of which can be probed experimentally, as in recent experimental work on double well quantum Hall systems.
I have also been interested in the effects of disorder and spin-orbit coupling on transport in the quantized Hall regime, and on some related problems of localization physics.