The effects of strong inter-electron interactions give rise to a remarkable range of anomalous behaviour in condensed matter systems, producing phenomena as varied as metal-insulator transitions, the fractional quantum Hall effect, high temperature superconductivity, and heavy fermion metals, insulators and magnets. The high temperature superconductors may even herald a breakdown of the fundamental Fermi-liquid theory of metals.
Although many theoretical models have been put forward as a basis for understanding these systems ,new mathematical techniques are required to provide results in the physically appropriate strong interaction regimes where many-body perturbation techniques are not applicable. In recent years non-perturbative methods have been developed and applied with great success to one dimensional and impurity models, and these have led to an understanding of the breakdown of Fermi liquid behaviour in one dimension.
The aim of this programme is to develop many-body approaches which can be applied to higher dimensional systems, and to remaining problems in one dimension such as transport, by bringing together experts from a wide range of mathematical approaches. Links with the experimental community in this field will be maintained, particularly through workshops and seminars.