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The resolution of the bounded L2 curvature conjecture in general relativity

Initial Data and Evolution Problems in General Relativity November 18, 2013 - November 22, 2013

November 19, 2013 (02:00 PM PST - 03:00 PM PST)
Speaker(s): Jeremie Szeftel (Université de Paris VI (Pierre et Marie Curie))
Location: MSRI: Simons Auditorium
Primary Mathematics Subject Classification No Primary AMS MSC
Secondary Mathematics Subject Classification No Secondary AMS MSC


Abstract In order to control locally a space-time which satisfies the Einstein equations, what are the minimal assumptions one should make on its curvature tensor? The bounded L2 curvature conjecture roughly asserts that one should only need L2 bound on the curvature tensor on a given space-like hypersuface. This conjecture has its roots in the remarkable developments of the last twenty years centered around the issue of optimal well-posedness for nonlinear wave equations. In this context, a corresponding conjecture for nonlinear wave equations cannot hold, unless the nonlinearity has a very special nonlinear structure. I will present the proof of this conjecture, which sheds light on the specific null structure of the Einstein equations. This is joint work with S. Klainerman and I. Rodnianski
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