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Explore the intersection of pure and applied mathematics in energy systems optimization through a captivating lecture by Dr. Claudia Sagastizabal. Delve into the management of energy systems, with a focus on the transition to sustainable electricity sources, and discover how interdisciplinary work is crucial for success. Examine the blurred lines between pure and applied mathematics when dealing with price signals in energy optimization. Follow along as the presentation unfolds through the lens of three influential mathematicians: Isaac Newton, Joseph-Louis Lagrange, and Jean-Jacques Moreau, whose contributions serve as archetypes in the field of energy optimization.