The Resolution of the Bounded L^2 Curvature Conjecture in General Relativity

Explore the resolution of the bounded $L^2$ curvature conjecture in general relativity in this 54-minute conference talk by Jeremie Szeftel at BIMSA. Delve into the fundamental question of minimal assumptions required to control a space-time satisfying Einstein equations. Examine the conjecture's assertion that $L^2$ bounds of the curvature tensor on a given space-like hypersurface should suffice. Trace the origins of this conjecture to recent developments in optimal well-posedness for nonlinear wave equations. Understand why a corresponding conjecture for nonlinear wave equations fails unless the nonlinearity possesses a specific structure. Gain insights into the proof of the bounded $L^2$ curvature conjecture, which illuminates the unique null structure of Einstein equations. Learn about the collaborative work with Sergiu Klainerman and Igor Rodnianski that led to this significant advancement in the field of general relativity.