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Explore a groundbreaking approach to the gluing problem in General Relativity presented in this 47-minute conference talk from the Thematic Programme on "Spectral Theory and Mathematical Relativity" at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into a novel perspective that leverages the nonlinearity of constraint equations to eliminate the 10-dimensional spaces of obstructions to gluing found in previous literature. Discover how this innovative method allows for the matching of two solutions of the Einstein equations along spacelike or characteristic hypersurfaces. Learn about the practical application of this technique, demonstrating that any asymptotically flat spacelike initial data set can be glued to Schwarzschild initial data of sufficiently large mass. Gain insights into this joint work with I. Rodnianski, which advances our understanding of mathematical relativity and opens new possibilities in the field of General Relativity.
