The last word in strong correlations
  In the Fractional Quantum Hall Effect (FQHE), in the noninteracting limit, only a fraction $\nu $ of the Lowest Landau Level (LLL) is occupied, producing a huge degeneracy. Interactions lift this degeneracy and mix in higher LL's. In the limit in which we ignore all but the LLL (i.e., let the inverse electron mass ${1 \over m}\to \infty$), the kinetic energy is an irrelevant constant and the ratio of potential to kinetic energy is essentially infinite, making this the most strongly correlated problem imaginable. I give a telegraphic review of the Hamiltonian Theory of the FQHE developed with Ganpathy Murthy that deals with this problem with some success. A nodding acquaintance with FQHE physics is presumed. 
R. Shankar
cond-mat.str-el