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Explore advanced concepts in conformal field theory through this comprehensive lecture that delves into the mathematical foundations and physical applications of CFT. Learn about conformal transformations, correlation functions, and the operator product expansion while examining how these theoretical frameworks apply to critical phenomena and string theory. Discover the role of conformal symmetry in two-dimensional quantum field theories and understand how conformal invariance constrains physical systems. Master key techniques for calculating conformal blocks, understanding conformal bootstrap methods, and analyzing the structure of conformal algebras. Examine specific examples of conformal field theories including minimal models and their applications to statistical mechanics and condensed matter physics. Gain insights into the connection between conformal field theory and other areas of theoretical physics such as AdS/CFT correspondence and quantum gravity, while developing the mathematical tools necessary for advanced research in this fundamental area of theoretical physics.
