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Explore the deep connections between gauge theory and integrability in this comprehensive lecture delivered at the International Congress of Basic Science 2025. Delve into advanced mathematical physics concepts as the speaker examines how integrable systems emerge within gauge theoretical frameworks, discussing the mathematical structures that link these two fundamental areas of theoretical physics. Learn about the sophisticated techniques used to identify and analyze integrable structures in gauge theories, including discussions of symmetries, conservation laws, and exact solutions. Discover how integrability methods provide powerful tools for solving complex gauge theory problems and gain insights into the broader implications for understanding quantum field theories and their mathematical foundations.
