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Explore the mathematical foundations of Liouville Conformal Field Theory and delve into the renowned DOZZ formula in this comprehensive lecture delivered at the International Conference on Basic Sciences 2025. Learn about the intricate connections between conformal field theory, quantum gravity, and mathematical physics as the speaker presents advanced concepts in theoretical physics. Discover how the DOZZ formula relates to correlation functions in Liouville theory and its significance in understanding two-dimensional quantum gravity models. Gain insights into the mathematical techniques used to derive and apply this fundamental result, including probabilistic methods and geometric analysis. Examine the broader implications of Liouville theory in modern theoretical physics and its applications to string theory and statistical mechanics.
