Phase Space Analysis of Partial Differential Equations

# The mathematics of General Relativity and nonlinear wave equations

speaker: Sergiu Klainerman (Princeton University)

abstract: The course gives an overview of some of the recent developments in the mathematical theory of general Relativity, in particular those in connection with the problem of evolution. I will concentrate in particular on recent results on the stability of the Minkowski space obtained in collaboration with F. Nicolo as well as some recent progress on the bounded L2 curvature conjecture obtained in collaboration with I. Rodnianski. We have recently have established a lower bound estimate on the radius of injectivity of null hypersurfaces imbedded, in Einstein spacetimes, which depend only on the flux of the spacetime ccurvature along the hypersurface. This is an important step in the proof of the conjecture and it is also important in its own right.

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