Geometric Analysis -- A Conference in Luminy, France, Winter 2011

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On January 17-21, 2011, there will be a one-week conference at Luminy, France on recent advances in geometric analysis, with the title `Geometric Analysis'. Within the general field of geometric analysis, the conference will focus on microlocal analysis, spectral geometry, conformal invariants, analysis on non-compact manifolds including the study of index theory and de Rham cohomologies as well as wave propagation, and the study of geometric flows. These topics are chosen because of many recent advances and numerous open frontiers, and because in spite of many connections between them, there is sufficient distance between these topics that collaborative projects, benefitting from different points of view, are particularly fruitful. In particular, the conference is expected to facilitate productive interactions between researchers working on elliptic and parabolic (which are the traditional strengths of the field), respectively hyperbolic (such as wave propagation), problems in partial differential equations. The proposal serves to provide for the transportation to the conference, and accomodation there, for some participants, with emphasis on graduate students, postdoctoral fellows, and junior faculty from US universities.Geometric analysis covers areas in which one studies phenomena, such as wave propagation or heat flow, on geometric backgrounds. One example of such a geometric background is general relativity, giving rise to a curved space-time of great physical interest. It also gives rise to `static' problems, without a `time' variable; the latter have received much of the attention as they are analytically more tractable. While often there is a physical motivation, recent work in the Ricci flow, which is an analogue of heat flow, shows that the field can also be used to answer questions of mathematical origin, in this case in topology (the study of shapes). This conference combines both aspects, and strives to encourage collaboration between researchers in different areas. It is also designed be ideal for doctoral students and young researchers as it will provide them with a host of techniques and problems relevant to their research. In particular, the speakers will be asked that the talks explain both the methods used and the motivations for the problem be it from a pure or an applied perspective, and there will be a discussion of new and open problems as well; this is expected to help young researchers just starting work in the field.