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Explore a mathematical lecture that delves into the quantitative stability of geometric inequalities, specifically focusing on the Prékopa-Leindler and Borell-Brascamp-Lieb inequalities. Learn how these functional extensions of the Brunn-Minkowski inequality from convex geometry refine the classical isoperimetric inequality and their fundamental importance in geometry, analysis, and probability. Discover recent breakthroughs in resolving long-standing questions about quantitative stability, particularly for the Prékopa-Leindler inequality, which had previously remained unsolved. Examine the collaborative research findings presented by Peter van Hintum from the Institute for Advanced Study, working alongside Alessio Figalli and Marius Tiba, during this Members' Colloquium session that bridges theoretical foundations with contemporary mathematical advances.
