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Explore the mathematical concepts of weaving and folding maps in this 50-minute conference talk delivered by Daniel Meyer from the University of Liverpool at the Fields Institute. Delve into the intricate relationships between dynamical, geometric, and random structures as part of the Fields-CNAM Nonlinear Days 2025 conference series. Examine how mathematical mapping techniques can be understood through the lens of weaving and folding operations, gaining insights into nonlinear mathematical processes and their applications. Discover the theoretical foundations and practical implications of these mapping concepts within the broader context of mathematical structures and processes.