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Seminar on
Mathematical General Relativity
Organizers:
S. Klainerman (Princeton)
P.G. LeFloch (Paris)
A. Zeghib (Lyon)
Fondations des Sciences Mathématiques de Paris
ANR Project
“Mathematical General Relativity. Analysis and geometry of spacetimes with low regularity”
Thursday June 14, 2012
Laboratoire J-L Lions
Université Pierre et Marie Curie, Paris
Lecture room 15-25 104
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11:00 am Jean-Philippe Nicolas (Brest) Perspectives in conformal scattering
Abstract. The origins of conformal scattering are to be found in a paper by Friedlander in 1980 “Radiation fields and hyperbolic scattering theory”, in which he realized that the Lax-Phillips theory was in fact providing an interpretation of scattering theory as the well-posedness of the characteristic Cauchy problem for the conformally rescaled wave-equation on null infinity. He clearly saw that the method provided an interesting geometrical short-cut to define a scattering operator with the advantage that all the analytical structure can be recovered a posteriori. The true power of the conformal approach to scattering theory lies in its complete indifference to time dependence. This talk will review the essential features of Lax-Phillips theory and its intimate link with conformal infinity via the Radon transform and the Whittaker formula, then describe the pinciples of conformal scattering with the crucial importance of the precise resolution of the Goursat problem; we will present some results (actual scattering constructions and studies of the Goursat problem) and explain the necessary steps of the extension of the method to black hole spacetimes, which is currently under development.
2:00 pm Jérémie Szeftel (Paris)
Abstract. TBA