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Explore a comprehensive lecture from Dr. Sven Krippendorf of Ludwig-Maximilians-Universität München that delves into learning mathematical structures through optimization problems. Learn how to discover symmetries and integrable structures in dynamical systems without prior knowledge, using phase space samples to uncover Lagrangians, conserved quantities, Lax pairs, and connections. Gain insights into the potential applications of these methods for finding numerical Calabi-Yau metrics. Part of the "Black holes: bridges between number theory and holographic quantum information" series, this 90-minute seminar demonstrates innovative approaches to understanding complex mathematical structures through modern computational methods.