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Prologue

This relatively large network of 15 groups with satellites in 12 countries has essentially been created by the two thematically close, but complementary former TMR networks Hyperbolic Conservation Laws and Asymptotic Methods in Kinetic Theory which had a successful research training collaboration e.g. by several joint TMR summerschools and conferences. Some key scientists of the thematically close TMR network Viscosity Solutions and Their Applications have been added to the new network, among them the former coordinator, a Fields medalist.

The important research training capacity and experience of these networks which is significantly enhanced by the synergetic joining to one coherent activity assert the capacity that HYKE is able to play a positive role for the European Research Area (ERA).

In accordance with the text of the call, the funding of 1.5 Million Euro has been exceeded purely for training need in order that each of the participating groups can host at least one young researcher for the 3 years. In fact, the HYKE teams with about 10 and more key staff members per team could easily deliver much more "European added value" research training.

The network is relatively big, in the sense of a flexible structure, not in the sense of a dinosaur~: e.g. this very community perfectly survived the major shock when about ten years ago one of its anchor projects, the HERMES space shuttle, was suddenly stopped for political reasons. Without any rupture or sign of being doomed, an immediate orientation to new applications took place. This flexibility is a central feature of the complementary and interdisciplinary mathematical training of HYKE. The applied mathematicians trained in this network will have the very geographic and scientific mobility which is vital in a changing globally competitive environment.

The size of the network yields a transition from quantity to quality in several respects :

1.) HYKE is a major global player in the field. It is a key part of an emerging worldwide network in mathematics, including centers like the IPAM in Los Angeles, the PI in Vancouver, the IMPA in Rio de Janeiro, the Morning Side Center of the Chinese Academy of Science in Beijing...

As a consequence, HYKE contributes to invert the brain drain to the US by helping to bring back young Europeans after a PhD or Post Doc in the US. Both the scientific standing of HYKE as such and the connections to top places in the US as well as the possibility of attractive salaries help to this end. In fact there are several young European mathematicians with PhD in places like Princeton for whom this RTN activity is most significant in their decision to come back before the age of 40.

2.) The complementarity and interdisciplinarity aspects are enhanced without losing the focus to one field of mathematical science where a common mathematical language is spoken.

3.) This network basically doubles the training months delivery per contract which is more efficient for everyone.

4.) Due to the size of HYKE, new management mechanisms are created, in particular the Training Committee which not only governs the research training activity independently of the rest of the management, but also implements a bottom-up mechanism of scientific training quality self control within RTNs.

5.) HYKE reaches a size that creates a new European added value : all members acquire an understanding for the meaning and problems of undertaking a truly European enterprise. Already the diplomatic setup of such a network structure and the joint proposal writing has been a contribution to the ERA.

The coordinator, out of his own mobility experience, e.g. as a B30 Marie Curie Fellow, makes a total personal commitment to the ERA and will implement voluntarily measures like structured collection of data e.g. on "obstacles to mobility".



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