This project consists of three research components in the general area of phase transitions and critical phenomena. These are: i) Discrete models of interfaces in three dimensions, including a study of surface fluctuations. ii) Percolation and related ferromagnetic models, including a study of (d+1)- dimensional models with d-dimensional disorder, which arise naturally from d-dimensional disordered quantum spin systems. iii) Spin glasses, including a study of the multiplicity of pure phases in short-range models. These mathematical studies are geared to develop an understanding of certain important physical and technological phenomena. Interface models arise in the study of wetting and lubrication. Disordered quantum spin systems are being extensively used to model the effects of impurities in superconductors. Spin glasses are closely related both to neural networks (an important development in artificial intelligence) and to large scale scheduling problems such as the famed "travelling salesman problem".
