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Explore the Cartan-Karlhede algorithm and its application to spacetime classification in this comprehensive lecture. Delve into the mathematical foundations that led to the algorithm's development for frame fields on manifolds and its adaptation to General Relativity. Examine the essential mathematical concepts required for implementation and learn how the algorithm generates Cartan invariants to classify solutions. Discover interesting applications of the Cartan-Karlhede algorithm in the field of gravity theories. Gain insights into the broader context of the SCREAM project, which focuses on Cartan and parabolic geometries and their interactions with mechanical systems, integrable systems, and cosmology.
