Final Activity Report Summary - TODEQ (Operator theory methods for differential equations) The ToK programme was hosted by the Institute of Mathematics of the Polish Academy of Sciences (as the only Contractor), within the period 1 April 2006 - 31 March 2010. The topics consisted of three related and interweaving tasks: 1. Semigroups and differential equations (task coordinator Yu. Tomilov); 2. Fine spectral theory of differential and difference operators (task coordinator J. Janas); 3. Operator theory methods for numerical analysis of differential equations (task coordinator T. Reginska). The training partners were University of Ulm, University of Bordeaux I, University of Lille, University of Oxford, and Helsinki University of Technology. Altogether 50 months of incoming MER and 24 months of incoming ER visits were realised, by 20 + 7 = 27 persons from 13 countries (including 4 non-EU countries). Also 20 months of outgoing MER and 18 months of outgoing ER visits to the training partners were realised, by 6 + 2 = 8 members of the IM PAN group. The Ministry of Science and Higher Education of Poland awarded the project by the maximal possible supplementary grant (based on the total contribution granted by the Contract between EC and IM PAN). This additional grant made it possible to realise a number of short visits, both incoming and outgoing, under more flexible rules, to participate in conferences and organise them, to buy necessary computers and literature, everything closely related with the project. This improved substantially the effectiveness of the project. In particular, we co-organised three conferences at our partners' sites, in Helsinki, Luminy, Oxford. Two conferences in Torun were devoted to task 1, and several workshops in Warsaw to task 3. Moreover, we co-organised many international conferences in Poland, as well as a regular Operator Theory Seminar at IM PAN in Warsaw attended by Polish participants from different cities and our visitors during the project. Some of the visitors gave talks also in Torun, Cracow, Lublin. The project was summarised at the final international conference "Operator theory and publications: perspectives and challenges", held on March 18-28, 2010 in Jurata, attended by 64 participants in the project. We also intend to publish a book in the Banach Center Publication series, based on the results of the project and stimulating further research, like our earlier volumes 30 (1994), 38 (1997) and 75 (2007) in this series. Actually some of these meetings were occasions to present courses of lectures devoted to dynamical systems, mathematical physics and biology, genetics, numerical analysis; altogether about 40 lectures attended usually by 30-40 participants. Members of the IM PAN group attended 103 international conferences, mostly giving (invited) talks. A large number of papers, mostly joint ones, were written during the project. In general, the project was very useful for continuation of our earlier scientific cooperation and for its further development, both in Poland as well as for our foreign partners.
