Explore a 53-minute lecture on the intrinsic flat stability of the positive mass theorem for graphical manifolds, presented by Raquel Perales from IMUNAM Oaxaca at the Institut des Hautes Etudes Scientifiques (IHES). Delve into the rigidity of the Riemannian positive mass theorem for asymptotically flat or hyperbolic manifolds, which states that the total mass of such a manifold is zero if and only if it is isometric to Euclidean or hyperbolic space, respectively. Examine the stability results obtained by Huang-Lee-Sormani, Allen-Perales, and Huang-Lee-Perales for asymptotically flat graphical manifolds using the intrinsic flat distance. Learn about an ongoing project with A. Cabrera Pacheco and M. Graf, investigating analogous results for asymptotically hyperbolic graphical manifolds.