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Explore fundamental programs and methodologies in representation theory through this comprehensive mathematical lecture delivered at the International Congress of Basic Science 2025. Delve into advanced concepts and theoretical frameworks that form the foundation of modern representation theory, examining key programs that have shaped the field's development. Gain insights into cutting-edge research directions and mathematical structures that connect representation theory to other areas of mathematics. Learn about the systematic approaches and methodological principles that guide contemporary work in this essential branch of abstract algebra and mathematical physics.
