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Explore advanced mathematical concepts in this 54-minute lecture from the Combinatorics of Fundamental Physics Workshop, where Institute for Advanced Study researcher Botong Wang delves into the intricate relationship between topology and algebraic optimization methods. Learn how topological structures influence optimization problems, examining theoretical frameworks that bridge pure mathematics with practical applications. Discover key insights into the mathematical foundations that connect combinatorial theory with fundamental physics, presented through detailed explanations and theoretical demonstrations at Wolfensohn Hall.