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The development or research partnerships towards European integration of the Romanian mathematical research in  the fields of nonlinear analysis, differential topology and their applications  (Contract  130/2006,  CEEX III/P-INT-VIZ)

This project has two fundamental components. On the one hand, one aims the enforcing of the long term scientifical and technical cooperation, through the creation of a complex European research network, ment to interconnect different research centres acting in the field at the European level. The cooperations that already exist between the members of our teams and experts from centres located in the European space, in countries as Austria, France, Germany, Italy, Poland and Hungary, are only the starting point for the development of a strong research network that will facilitate a better integration of the research effort as well as a correlation of the specific national research programmes from the field. The feedback obtained after launching the project proposal from the prospected partners, emphasizes both the timeliness of this initiative and the support it enjoys among the well-known experts in the field. In this way, the project will contribute to the endorsement of the European Research Area (ERA) and to the achievement of the objectives of communitary policy in the field of RDI. On the other hand, we have in mind the increase of the visibility of the top Romanian mathematical research, as well as the capitalization of the competences and the research potential existent at the Babes-Bolyai University from Cluj-Napoca, through direct contacts, exchanges of ideas, opinions and experts, as well as by the organisation of far-reaching scientifical events, summer schools and conferences, some of them, the Sophus Lie seminary, organised for the first time in Romania. One foresees both research stages of the members of the team and the invitation of some leading experts from the area specifical to this project, in order to create a real research network through which to realize a permanent and effective interconnection to the main flow of scientific ideas and results which are circulated now through the top research centers of Europe.

The themes tackled in this project cover a broad spectrum of domains of mathematics which are currently under intense investigations, including variational calculus, critical point theory, noncommutative geometry, and their applications (for instance to the study of differential equations or to theoretical physics), cyclic homology and noncommutative geometry.

This projects starts from the premise that the obtaining of scientific results and their dissemination are not enough for the integration of a research center in the European conscience. This integration has a solid scientific component, but also a social and a cultural one. To this end, we stipulated, beside the research stages of the members of our team in the centers mentioned above and the capitalization of the competences and the research potential existent at the Babes-Bolyai University and in Romania, the attraction of prestigious researchers from the international (and especially European) scientific community, as well as the preparation of some common projects for the future FP7 program of the European Commission.

We have in view the increasing of the attractivity of the mathematical research for future generations of researchers, by opening concrete research opportunities for young researchers, as well as by bringing of the present-day undergraduate, graduate and PhD students at the level of knowledge which is objectivally necessary to have the possibility to participate afterwards, in an active manner, in the extended framework of this research area.