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Explore a concise proof of the Alexandrov-Fenchel inequalities for mixed volumes of convex bodies in this 42-minute lecture. Delve into the collaborative work of Klartag, Cordero-Erausquin, Merigot, and Santambrogio as they present a novel approach to this fundamental concept in convex geometry. Gain insights into the mathematical techniques and reasoning used to establish these important inequalities, which have wide-ranging applications in various fields of mathematics and physics.
