Around the Alexandrov-Fenchel Inequality - Convex Geometry and Its Applications

Explore the fascinating world of convex geometry in this 54-minute lecture by Ramon Van Handel at BIMSA. Delve into the history and recent developments surrounding the Alexandrov-Fenchel Inequality, tracing its roots back to Hermann Minkowski's groundbreaking work in the late 1800s. Discover how Minkowski's study of convex sets revolutionized our understanding of geometry, leading to surprising connections with classical problems in number theory. Learn about the generalization of the isoperimetric theorem and the intriguing "bubbles" that emerge when fixing different geometric parameters. Gain insights into recent progress made by Van Handel and Yair Shenfeld on long-standing problems in this field. Uncover the wide-ranging implications of these geometric concepts across various mathematical disciplines, including analysis, algebra, combinatorics, and computational complexity.