We hope that that transfer of knowledge between partner organisations, IMPAN, and the outside researchers participating in the programme will help to strengthen the capabilities of the involved researchers in very advanced mathematical methods and in some applications (population dynamics, fractals, blood motion). The aim is to strengthen interdisciplinary contacts. This should increase the potential of mathematics serving as a modern tool and language for other scientific disciplines. In the longer term this should have positive impact on technological development.
The main aim is to strengthen the existing ones and create new areas of competence in the research and educational activities of the Institute in selected branches of mathematics linked together. Let us again list these newly emerged areas:
NSE asymptotic behaviour in time and space (non-regular domains) 3D-thin or axically symmetric (blood vessels). Geometric measure theory in multifractal analysis of attractors in NSE. Scaling limits in physical processes, see B1. They will be developed basing on our knowledge and experience in dynamical systems, theory of functions and stochastic processes.
Long term visits of carefully selected specialists working in these subjects will have a direct impact, increasing our capacity for fruitful research and teaching mathematics, see B.5 and B2.1. We plan to invite the strongest specialists in the world (some of them visited already
Poland) J.-Ch. Yoccoz, J. Pisier, K. Gawedzki, A. Kupiainen, S. Smirnov.
The Banach Center and IMPAN are known for their significant past contribution to the European mathematical community. We have to make a considerable effort to conserve this status when the political and economical situation of Poland is changing (joining the EU). This is one of the main purposes of the action of transfer of knowledge described in this proposal. We believe that thanks to such programmes IMPAN and its branch, the Banach Center, will become one of the leading mathematical institutions in Central Europe. This together with the further increase of European cooperation should prevent the transoceanic brain drain of talented young mathematicians. This will help some outstanding Polish mathematicians working abroad to make the decision to re-immigrate to Poland.
We expect one more positive effect of the multidisciplinary character of the programme. Its realisation should strengthen the cooperation between local teams working in the areas of the programme. The lectures and seminars given by visiting specialists will gather specialists from different groups, discussing common problems. The programme of transfer of knowledge is o special importance for graduate students and young researchers. Direct contact with the leading specialists will help them to choose their subject of research and to establish international contacts.
It is crucial in mathematical research to have access to the most recent techniques and results obtained by other research groups. The most effected transfer of knowledge is by direct contacts with the leading specialists. In order to acquire new techniques usually it is sufficient to have one or more relatively short visits when teaching duty is not required. Therefore we plan the typical secondment to last 2-6 months and typical visit in Warsaw to last 6-12 months.
We are conscious that the large number of 5 partner institutions forces visits to some of them to be relatively short and allows only one visit. The partner institutions have been chosen by us as a result of thorough consideration and the choice follows from the multi-disciplinarity of the project. We have decided that in view of our needs and EC policies it is appropriate to concentrate more on incoming foreign scientists.
The experience of our Centre of Excellence (and Banach Center) shows that leading foreign scientists willingly visit us, due to the enjoyable environment found here, often for long stays.
However in many cases it is difficult for more experienced researchers to be on leave for a long time. So we plan to split up visits in this category into shorter periods.
The proportion 30:36 visits at IMPAN is a delicate consensus between desire to invite (under competition) top YR which is of our highest priority to create a young dynamical new school, and more experienced researchers necessary to teach the advanced areas of the ToK.