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Explore the mathematical foundations of Carroll flux-balance laws and their applications in flat-space holography through this advanced theoretical physics lecture. Delve into the intricate relationship between Carroll geometry and holographic principles, examining how flux-balance equations govern the dynamics of field theories in flat spacetime backgrounds. Learn about the theoretical framework that connects asymptotic symmetries, boundary conditions, and conservation laws in the context of holographic dualities. Investigate the mathematical structures underlying Carroll manifolds and their role in understanding gravitational theories at null infinity. Analyze the derivation and implications of flux-balance laws, their connection to soft theorems, and their significance in modern approaches to quantum gravity and holography beyond anti-de Sitter spaces.
