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Explore the intricate connections between Riemann geometry, topology, and physics in this doctoral-level lecture, the first of a two-part series on "Interdisciplinary Frontiers of Theoretical Physics." Delivered by Renzo Ricca at the Beijing Institute of Technology, this 75-minute presentation delves into advanced concepts that bridge mathematical and physical theories. Gain insights into how Riemannian geometry and topological principles apply to complex physical systems, enhancing your understanding of cutting-edge theoretical physics research.