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Explore the complex issue of lake eutrophication and learn about optimal control strategies in this 58-minute lecture from the Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC). Delve into the ecological challenges posed by excessive nutrient enrichment in lakes and discover cutting-edge approaches to mitigate its harmful effects. Gain insights into mathematical modeling techniques used to analyze and predict eutrophication processes, and understand how these models can inform effective management decisions. Examine case studies of successful lake restoration projects and discuss the application of optimal control theory in developing sustainable solutions for maintaining healthy aquatic ecosystems. By the end of this lecture, acquire a comprehensive understanding of the interdisciplinary approaches required to address one of the most pressing environmental issues facing freshwater systems worldwide.