Mathematical medicine, notably tumour growth and treatment, bacterial infections, drug delivery, tissue engineering and cell signalling. Industrial mathematical modelling Development of asymptotic (including exponential asymptotic) and exact techniques for the study of linear and nonlinear differential equations. Development and analysis of models for nonlinear diffusion, in particular. Analysis of moving boundary problems, particularly with respect to singularity development. Development, analysis and application of evolution equations for thin-film flow. Pattern formation in diffusive systems.