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Explore the intricate connections between topological 5-dimensional N=2 gauge theories, mirror symmetry, and Langlands duality through this advanced mathematical physics lecture delivered at the ICBS2025 conference by BIMSA. Delve into the sophisticated mathematical framework that links A-infinity categories of Floer homologies with these fundamental concepts in theoretical physics and algebraic geometry. Examine how mirror symmetry manifests in the context of five-dimensional supersymmetric gauge theories and discover the profound relationship between geometric Langlands correspondence and topological field theories. Investigate the role of Floer homology in understanding the categorical structures underlying these dualities, and learn how A-infinity categories provide the appropriate mathematical language for describing these complex relationships. Gain insights into cutting-edge research at the intersection of algebraic topology, representation theory, and quantum field theory, suitable for advanced graduate students and researchers working in mathematical physics, algebraic geometry, or related fields.
