Orateur
Jérémie Szeftel
Description
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 bounds of the curvature tensor on
a given space-like hypersurface. 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
talk is intended for a general audience and will require no specific
background. This is joint work with Sergiu Klainerman and Igor
Rodnianski.
