The Mysterious Extremals of the Alexandrov-Fenchel Inequality

Explore the fascinating world of convex geometry in this lecture on the Alexandrov-Fenchel inequality and its mysterious extremals. Delve into the long-standing open problem of characterizing equality cases, dating back to the works of Minkowski and Alexandrov. Discover recent breakthroughs in characterizing extremals for convex polytopes, completely settling the combinatorial aspect of the problem. Learn about key insights from the proof, potential applications in extremal combinatorics, and the challenges in extending results to general convex bodies. Gain a nontechnical understanding of this central result in convex geometry and its deep connections to other areas of mathematics, with minimal background required.

Ramon van Handel: The mysterious extremals of the Alexandrov-Fenchel inequality