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Dive into an extensive 2-hour and 50-minute lecture on advanced mathematical concepts, focusing on the fourth installment of the Introduction to Topological Recursion series. Explore complex theoretical frameworks and mathematical principles as presented by experts from IPhT-TV. Gain in-depth knowledge of topological recursion and its applications in various fields of mathematics and theoretical physics. Enhance your understanding of this sophisticated topic through detailed explanations, examples, and potential real-world applications. Suitable for graduate students, researchers, and professionals in mathematics, physics, and related disciplines seeking to expand their expertise in topological recursion theory.