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Explore the intricate connections between quantum analytic Langlands correspondence, complex Chern-Simons theory, and supersymmetric quantum field theory in this advanced mathematical physics lecture delivered at the International Congress on Basic Sciences 2025. Delve into the sophisticated mathematical frameworks that bridge algebraic geometry, representation theory, and theoretical physics as the speaker examines how these seemingly disparate areas of mathematics and physics interconnect through deep structural relationships. Investigate the quantum extensions of classical Langlands correspondence and understand how complex Chern-Simons theory provides a geometric framework for understanding these connections. Learn about the role of supersymmetric quantum field theories in providing physical realizations of these abstract mathematical concepts, and discover how these theories contribute to our understanding of both pure mathematics and theoretical physics. Gain insights into cutting-edge research that sits at the intersection of number theory, algebraic geometry, and quantum field theory, suitable for advanced graduate students and researchers in mathematical physics, algebraic geometry, and related fields.
