The investigations into the statistical mechanics and quantum field theory of systems with an infinite number of degrees of freedom will be continued. In the past year a major discovery in statistical mechanics was made by finding that many of the N state chiral Potts models used in the study of commensurate incommensurate phase transitions are solvable in the sense of possessing a one parameter family of commuting transfer matrices, and that these transfer matrices are parametrized by curves of genus greater than one. Such models, based on higher genus curves, have been searched for over fifteen years and their discovery opens new areas of research both in solid state physics and in the related area of algebraic geometry. During the course of this award studies will be made of the free energy and excitation spectrum of these models and their correlation functions, particularly in their connection with conformal field theory. They will also continue to search for more models based on curves of genus higher than one and to investigated whether such models can be found in three dimensions. Investigations of the relation between these new models, the methods of deformation theory, and possibly string theories will be made.
