9714055 Girvin With a wide ranging title, this is a multi-project grant to consider a large variety of current problems in condensed matter theory. The group which these PI have assembled at the Indiana University, is generally acknowledged as a leader in numerous forefront problems. This renewal grant contains projects on phase transitions in Josephson junction arrays, on an analysis of possible numerical methods incorporating both the density matrix renormalization group and also the dynamic mean field theory, possibility of a skyrmion lattice phase transition, quantum phase transitions at very low temperatures, superfluid 4He in confined geometries where it is believed to be a prototype for the complex interplay between strong correlation and disorder, quantum Hall edge states and ultra-small superconducting grains. %%% This grant continues to support the cutting-edge work of these two senior PI's. They are acknowledged as amongst the world's best in innovative research, effective nurturing of younger students and colleagues and community service, including the recent panels at NRC and at NSF. Their research program spans a broad spectrum of topics including electron gas (and superconductivity) at high magnetic fields, attempts to improve numerical techniques and superconductivity in ultra-small particles. ***
