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Explore the mathematical foundations of derived conformal field theory in this 57-minute conference talk that delves into advanced theoretical physics concepts. Learn about the mathematical structures underlying conformal field theories through a derived algebraic perspective, examining how derived categories and homotopical methods can be applied to understand CFT more deeply. Discover the connections between derived algebraic geometry and conformal field theory, including discussions of derived functors, spectral sequences, and their applications to physical theories. Gain insights into cutting-edge research that bridges pure mathematics and theoretical physics, particularly focusing on how derived methods can provide new tools for analyzing conformal field theories and their properties.