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Explore a comprehensive mathematical lecture examining stability questions in geometric and functional inequalities through the lens of optimal transport theory. Delve into foundational concepts that have shaped analysis and influenced understanding of mathematical and physical phenomena, with particular focus on quantifying how close nearly optimal functions are to genuine minimizers. Discover how optimal transport provides a powerful framework for addressing stability questions in various mathematical contexts, while also learning about scenarios where alternative approaches may be more suitable. Gain insights from cutting-edge research that bridges classical inequality theory with modern optimal transport methods, presented as part of the prestigious Green Family Lecture Series at the Institute for Pure & Applied Mathematics.
