Stochastic Partial Differential Equations arise naturally as models for those physical and biological problems in which one is modelling a stochastically evolving distribution over a continuous space. The programme will develop the strong mathematical foundations on which the theory rests and provide an introduction to techniques borrowed from other areas of infinite dimensional stochastic analysis. It will also cover some of the important areas of application; much of the early work on SPDE was motivated by the Zakai equation of nonlinear filtering and more recent work has been inspired by problems as diverse as understanding the early evolution of the Universe and oil extraction.
The programme is principally concerned with mathematical and physical models of solid-liquid continua with emphasis on the effects of phase-change. The aim of the programme is to bring together leading workers from different disciplines (experimentalists, geophysicists, mathematicians, metallurgists) to encourage a cross-fertilization of approaches. The primary goal will be to identify the dominant physical processes and so determine the correct macroscopic equations and boundary conditions that relate to phase-changes in a variety of both pure and multi-component systems. The programme will be founded on a core of about ten scientists drawn from the various disciplines and, during the first week, these researchers will contribute to an instructional programme for young researchers. A workshop dealing specifically with the macroscopic manifestations of solid-liquid systems will last some seven days beginning in the second week and will concentrate on the topics of phase ! coarsening, convection, compaction, magmas, mushes/slushes/slurries and phase field models. To close the programme there will be a three day conference that is to be more broadly based embracing, for example, phase-change systems such as solid-solid and liquid-gas systems.
The theme of the programme will be the interaction between complex analysis, complex geometry and differential geometry. The programme will consist of a workshop with different topics centred during different periods, followed by a two-week concluding conference.
Our aim is to bring together researchers who use complex methods in diverse branches of differential geometry. Such methods have been at the heart of many recent advances and we feel that an opportunity for further interaction would be both timely and fruitful. We intend to focus on three main areas:
D V Alekseevsky, J P Bourguignon, D Burns, S Donaldson, E Grinberg, V Guillemin, N Hitchin, B Lawson, L Mason, S Merkulov, M Micallef, R Penrose, S Salamon, G Tian, J Wolf.