Rafael Olaprath: Asymptotic analysis of isolated gravitational systems and the ADM center of mass

A (very early-stage) analysis of Asymptotically Euclidean solutions to the Einstein Constraint Equations, with special consideration to the solutions that are conformally flat at infinity as obtained by Justin Corvino. In the same vein, we also discuss the Yamabe problem and its solution briefly, concluding with an outlook entailing further development of solutions.