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Explore the fundamentals of tensor networks and their applications to many-body quantum systems in this comprehensive lecture from IPAM's Quantum Winter School 2026. Delve into the mathematical framework of tensor networks as powerful computational tools for studying complex quantum many-body problems. Learn how these networks provide efficient representations of quantum states and enable the simulation of strongly correlated systems that are otherwise intractable with classical methods. Discover the theoretical foundations underlying tensor network methods and understand their role in advancing quantum simulation capabilities. Gain insights into how these techniques bridge the gap between theoretical quantum mechanics and practical computational approaches for analyzing many-body phenomena. This first part of a two-part series establishes the essential concepts and mathematical structures that form the basis for more advanced applications in quantum simulation and condensed matter physics.
