Spade2 ♠♠ deterministic and stochastic dynamics, fractals, turbulence

B2.1. Need for training and transfer of knowledge

For many years Polish science has been suffering from significant under-funding and the resulting brain drain of smart young researchers, mainly to the USA. Consequently there is a drastic need to remedy this situation. This can be done among others by a better participation of Polish scientists in the mainstream of research in several fields of great importance. Recent breakthroughs and new mathematical techniques, if adopted promptly in Poland, should increase the potential of Polish, and hence European, mathematics and its positive influence on the development of other fields.

A high level of knowledge in the analytic areas of mathematics usually correlates with the high level of technology and education in the engineering schools. We expect our ToK programme will have such an impact since PhD students and researchers of the Warsaw Technical University (which is located 200 m from IMPAN) are expected to participate in the activities of it. The topics of SPADE2 are selected not only to foster specialised research, but also to increase the mathematical analysis and stochastic processes knowledge/culture among engineers.

The project is of interdisciplinary character, so to foster technological development it is necessary to promote the interest of young researchers in this area. The topics of the project include very advanced, technically difficult theories. Even for experienced researchers it is important to learn this through direct contact with very top specialists who know the subject, its background, the motivations and relations to other subjects. It is also important to expose and discuss our own results with leading specialists and other younger colleagues.

Interest at the European level.

To be technologically competitive, Europe must organise and promote scientific activities in mathematics and applications, in particular in the SPADE2 areas. The Banach Center and IMPAN have a good location and perfect work conditions, including the main tool of a mathematician: the excellent library which has survived many economical and political turns. The Banach Center has long record of exchange of knowledge in mathematics but has little funds for medium term visits of external researchers, to attract them it should offer decent salaries (much higher then the standard salaries in Poland), not affordable within IMPAN budget, see below and B5,2. The scientific career is still in some esteem in Central-Eastern Europe and scientific potential is large attracting young candidates for research. Europe should not allow this to be lost!

Explanation of >4,>10, and "in", "out" mixture

The employment policy of IMPAN includes the rule that young (post-doc) researchers (coming from universities) are offered 1 - 2 year positions which are extended to longer periods only in exceptional cases. On the other hand IMPAN employs more experienced (post habilitation) researchers for longer contracts. Furthermore most of the knowledge we wish to import is on the cutting edge of sophisticated and advanced research. We thus plan to devote more person/months for visits and secondments of more experienced researchers.

We plan to invite 2 researchers for 1 year term and 12 for 2-6 months.

Planning 66 person/months visits of experienced and more experienced researchers during the programme, we expect usually 2 visitors from abroad at any time. They can lead or co-lead 2 seminars and together with local students and local researchers they will create a critical mass to achieve significant results. To increase the availability of the top experts in the field, we intend to offer contracts that would cover several months, but can be split up into parts.

46 person/months of visits in partner institutions will provide ten short-term (2-6 months) visits.

B2.2. Content of the Transfer of Knowledge

IMPAN has organised seminars and lectures regularly for many years. They attract an audience from the whole of Poland with many talks given by foreign specialists. We would like to link each of the lectures of the proposed specialist with an established seminar. We hope that this will ensure a large audience for both seminar and lecture. Some seminars will be reorganised, to fit better the needs of the programme. We list existing seminars, which will be hopefully reinforced, due to the programme. In square brackets we indicate the leaders of the seminars.

1. General seminars:

• 
  Population dynamics (all the Tasks, Katowice/Warsaw) [R.Rudnicki, A. Lasota]
  

• 
  Dynamical systems (Task 1, in relation with 2,3)[H. Żołądek, A. Zdunik, F. Przytycki]
  

• 
  Partial Differential Equations (Task 2) [B. Bojarski, W. Zajączkowski, G. Łysik, G. Łukaszewicz, Z. Peradzyński, J. Grabowski]
  

• 
  Stochastic Processes (Task 3) [J. Zabczyk, Sz. Peszat, T. Komorowski]
  

• 
  Functional Analysis (Task 4) [A. Pełczyński, Cz. Bessaga, W. Żelazko, S. Rolewicz, S. Kwapień, R. Latała and others]
  

• 
  Spectral Theory of Differential Operators (Tasks 2, 4, Kraków branch) [J. Janas]
  

• 
  Approximation Theory (Tasks 2,4, Gdańsk branch [Z. Ciesielski, A. Kamont, T. Figiel]
  

and several other seminars at Warsaw University and Warsaw University of Technology

2. Special interdisciplinary seminar:

We plan to organise a multidisciplinary weekly seminar being a series of colloquium talks in all the tasks of the programme. This will be coordinated with the traditional series of Colloquia by Banach Center, IMPAN and the Polish Mathematical Society.

3. Some specific seminars (existing or planned):

• 
  Analytic theory of differential equations (Task 2)[G. Łysik, H. Kołakowski]
  

• 
  Geometric Theory of Sobolev spaces (Task 4) [P. Hajłasz, P. Strzelecki, A. Kałamajska]
  

• 
  Wavelet bases in function spaces (Task 4) [P. Wojtaszczyk]
  

• 
  Navier-Stokes Equations (Task 2) [W. Zajączkowski]
  

• 
  Holomorphic iteration (Task 1) [J. Kotus, F. Przytycki, A. Zdunik]
  

Several (1-semester or longer) courses or series of advanced lectures given by the scientists involved in ToK will be provided. We mention only some of them:

• 
  Homoclinic tangency bifurcations (Task 1)
  
• 
  Point processes and their applications (Task 3.)
  
• 
  Evolution equations (all Tasks)
  
• 
  Unconditionality of spline bases (Task 4)
  

Scientists involved in the ToK will give short courses and survey lectures at mathematical weekend seminars (national), Banach Center research schools, summer schools and workshops (international).

4. Tutoring

Tutoring related to the courses will be delivered by the visiting scientists, to local young researchers (in order that the young participants and tutors master the topic).