Topological Quantum Numbers

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This award supports fundamental research and education in systems, which have topological quantum numbers. The proposed work is focussed on the dynamics of vortices in superfluids and superconductors, mechanisms for flux flow at low temperature, the structure of surfaces and interfaces of fractional quantum Hall phases, and the nature of transitions between quantum Hall phases. This award supports graduate education of students in condensed matter theory and theoretical research focussed on two important problems that lie at the frontiers of condensed matter theory that have a subtle geometric connection. These are the motion of vortices in superconductors, and phase transitions between novel quantum states that occur in electrons trapped at semiconductor interfaces in high magnetic fields.