Since almost ten years, numerous connections have been made between teams of pure or applied mathematicians working in the field of PDE and teams of theoretical physicists who demonstrate mathematical results for spectral or scattering theory in Quantum Mechanics.
This has led progressively to interactions and collaborations where the methods of microlocal analysis have proved able to refine results for Schrödinger operators and provide new results for quantum systems of present physical interest notably in supraconductivity. In the reverse direction, so to say, methods of quantum mechanics that were more specifically devised by "theoretical physics'' teams have been developed and generalized to larger mathematical problems, thus opening new research fields. We can mention (with no aim at exhaustiveness) the so-called "commutator method of Mourre'', the "dilation analyticity method'' for the study of resonances, the application of non-commutative geometry to the quantum Hall effect, the "coherent states method'' in semiclassical analysis... In addition a number of tools of functional analysis proved to be fruitful not only for linear Schrödinger equation but also for nonlinear PDE of physical relevance like the nonlinear wave equation, the nonlinear Schrödinger and Klein-Gordon equation, etc...
This new synergism has been reinforced by annual meetings which have more specifically federated the aspects of microlocal and semi classical analysis : the so-called "Journées Semiclassiques".
They have been organized successively by various universities of France, with national and local financial support, including CNRS. Moreover, they got a more and more pronounced european character, being enriched from the numerous collaborations that the french teams had with their partners in the departments of mathematics or theoretical physics of universities of other european countries.
Now the European GDR MPhiQ has been functioning since January 2001. It has strongly reinforced the synergy between the different participating teams. It has also allowed an habit of exchanges and common work, in particular for the youngest researchers who became involved recently in these scientific fields (they constitute nearly the half of the "work force" of this Group of Research).
Now the GDR federates 25 teams in France, (among them 9 of theoretical physics), and 19 in Europ outside France (10 in theoretical physics).
These goals will be pursued for a new period of the 4 years, namely till the end of 2008. 6 new teams have decided to join the GDRE, which gives to it a new impulse. The true European dimension will be concretised by a GDR meeting organized by one of the European Universities close to France (Bologne) in 2006.
The GDRE (french acronym) will be organized around one or two meetings per year, which will be held each year in a different University of France (or close to France) easily accessible by european transportations.
The scientific orientations of the GDRE (notably the choice of lectures, speakers and place of meeting) will be defined by a "Group Committee" composed of ten to fifteen scientists (Mathematicians and Theoretical Physicists). See the joint list.
The contacts between the teams will be ensured by one coordinator per team. It has seemed judicious that these coordinators are chosen among researchers who are sufficiently young, so that they are not overburdened by other tasks, but experienced enough to fulfill their animation role. They will also have the responsability to make propositions to the "Group Committee", according to their teams' expectations.
The financement of the GDRE is only devoted to the participation fees to the annual meetings of the GDRE. It will ensure a particular support to young researchers. The secretarial work will be ensured by the "Institut de Physique Nucléaire de Lyon''.