The outcome of this proposal will be a series of three very high level Euro Summer Schools in Mathematical Analysis. The principal aim of the series is the training of young researchers from the EU and Associated States, to provide them with the information and contacts to further their research over the next decade. Mathematical Analysis is an area of central importance within mathematics, and in this series it is intended to treat three topics - MATHEMATICAL ANALYSIS OF HYDRODYNAMICS, OPERATOR THEORY, and ANALYSIS AND COMPUTATION: THEORY AND ALGORITHMS.
Each of these reaches out not only to other areas of analysis, but also to other areas of mathematics, science and technology. These topics are at the forefront of current international developments. Each Summer School will consist of around 15 lecture courses, usually in the form of three one-hour lectures, given by leading international experts who are also renowned for their expository skills. The formal lectures will also be supplemented by tutorial sessions. Eighty participants are expected to attend each Summer School, with around 40 to be funded through this proposal. The Summer Schools will last 11 to 12 days and will be carefully structured so that the more elementary and familiar material is presented first, and the cutting-edge state-of -the-art research at the end. The host organisation - the International Centre for Mathematical Sciences (ICMS) - has over a decade of experience in hosting research level conferences of many sorts. In particular, every year since 1993, it has organised instructional courses in analvsis of a verv similar type and scale to those proposed here.