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Explore the asymptotic structure of gravity in asymptotically flat contexts at spatial infinity through Hamiltonian methods in this comprehensive lecture. Delve into the main ideas behind the Poisson bracket algebra of BMS charges and discover a supertranslation-invariant definition of angular momentum. Presented by Marc Henneaux from the Université libre de Bruxelles at the Institut des Hautes Etudes Scientifiques (IHES), this 1-hour 29-minute talk is the first of two lectures on the subject. Gain insights into the connection between spatial infinity and null infinity, and understand the justification for Strominger's matching conditions of fields between past and future null infinity.
