This programme will emphasise selected recent developments in nonlinear elliptic and parabolic partial differential equations, together with geometric and scientific applications. It will be divided into four interrelated themes:
Reaction diffusion equations - Particular attention here will be given to transition layers and their applications.
Fully nonlinear equations - This area has developed substantially over the last two decades. Emphasis will be on Monge-Ampère equations and viscosity solutions.
Variational problems with singularities - This theme will focus on mathematical models arising from material science, particularly from superconductivity and liquid crystals.
Geometric evolution equations - The mathematical study of flows determined by geometric quantities has blossomed in recent years, with striking applications to areas such as image processing and relativity.