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Explore advanced applications of tractor calculus in general relativity in this comprehensive lecture by Dr. Jarosław Kopiński from the Center for Theoretical Physics PAS. Delve into the utilization of tractor calculus for studying specific classes of spacetimes with prescribed asymptotic behavior. Begin with an overview of fundamental tractor calculus concepts and their relation to conformal infinities. Examine the concept of higher fundamental forms and their application in characterizing the conformal boundary of asymptotically de Sitter spacetimes. Investigate the geometric implications of spacetime possessing an initial isotropic singularity. Discover a general method for matching spacetimes in Penrose's Conformal Cyclic Cosmology model. This lecture is part of the SCREAM project, focusing on Cartan and parabolic geometries and their interactions with mechanical systems, integrable systems theory, and Penrose's Conformal Cyclic Cosmology programme.
