1 January - 19 June 1997

**Organisers**: D Olive (*Swansea*), P Van Baal (*Leiden*), P West (*King's College, London*)

Recent results of Sen, Seiberg and Witten have made increasingly plausible the idea of a quantum transformation between the weak and strong coupling regimes of spontaneously broken supersymmetric gauge theories in four space-time dimensions. The relevant ideas encompass and unify many topics studied intensively over recent years by particle physicists including QCD and the theory of instantons, solitons and their quantisation, conformal field theory, Yang-Baxter equations, the s and t duality of string theory and the mirror symmetry of Calabi-Yau manifolds. The new results have also already had an impact on pure mathematics, for example in the understanding of the Donaldson classification of four manifolds. The aim of the programme is to exploit the idea of electromagnetic duality to gain new insights into fundamental physics (for example, the issue of confinement in QCD), condensed matter physics and pure mathematics.