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Each university is far from covering the entire spectrum of a research area. Therefore, the CNRS plays a vital and cross-cutting role in coordination and stimulation within its area of fundamental research ; it still incites its research units to develop applications of the fundamental results obtained as well as of the know-how acquired, including that gained through industrial partnerships.

From early 2009, the CNRS will delegate a more or less important part of that work to the Institute for Mathematical Sciences and their Interactions (“Institut des Sciences Mathématiques et de leurs Interactions” – InSMI). We are not able to describe its role, since the actual arbitration concerning its degree of autonomy, or its missions, has not yet been made. What is certain is that things will not be as before. Here is how the CNRS plays its role today.

The CNRS approves Joint Research Units (“Unités Mixtes de Recherche” – UMR). It appoints researchers, engineers, technicians and administrative staff to the UMR, as well as provides them with various tools. It creates Research Networks (“Groupements de Recherche” – GDR), which are responsible for uniting temporarily a national community on a promising subject, and Federations of laboratories which are geographically close. It implements many tools of international cooperation and tools to assist research. It supports and provides funding for research initiatives which are innovative and risky.

In mathematics, the CNRS has about 350 researchers and 200 Engineers, Technicians, and Administrative staff who are primarily assigned to laboratories at universities. Mathematics represents 47 UMR, 24 GDR and 5 CNRS Federations.

A UMR in mathematics covers most of the time a whole mathematics department of a university, sometimes even two or more universities. In large concentrations of mathematicians in Paris, one may find UMRs which cover specific research areas, but in all other places the idea is to gather all of the mathematicians of a given site, from the most abstract to the most applied approaches, in order to encourage meetings and exchanges ; the most unexpected collaborations being often the most innovative. The policy of the CNRS in mathematics was to ensure that, throughout the country, as many academics as possible are attached to a UMR, in order to have reasonable means to conduct research and to keep in touch with other mathematicians in their field. In order to achieve these goals, every person in charge of the mathematics at the CNRS has tried for at least fifteen years to develop contacts with those in charge at the partner universities. It should be emphasized that the latter are almost always eager to develop cooperation.

The numerous GDRs are each designed to bring together a community of mathematicians, either in a sub-discipline or around emerging themes that require the implementation of varied skills. One of their main objectives is to contribute to the training of Ph.D. students and young researchers, as well as their integration into the world of professional researchers.

The Federations in mathematics have several aims : to develop cooperation between mathematicians in the same region by connecting certain Host Teams (not directly attached to the CNRS), to give them access to certain resources of the CNRS and to insert them into the doctoral training programs ; to promote mathematics from a given region in the eyes of local administrative authorities who finance research ; finally to set up partners for the Poles of Research and Higher Education (“Pôles de Recherche et d’Enseignement Supérieur” – PRES) which are being formed. In this area the CNRS’s objective is to move towards the setting up of federations, mostly regional, wherever they do not exist and where it is possible to establish them.

The international cooperation is based on the European Research Network (“Groupement de Recherche Européen” – GDRE) and on Joint International Units (“Unité Mixte Internationale” – UMI), which are specific to the mathematics by involving computing or physics ; as well as on the common resources within the CNRS which are the Platforms for Internet Content Selection (PICS – traduction ?!..) and the bilateral cooperation.

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