Kahler Packages on Valuations on Convex Sets and Their Applications

Explore a mathematical lecture where Semyon Alesker from Tel Aviv University delves into the intricate world of valuations on convex sets, focusing on Kahler packages and their practical applications. Learn about finitely additive measures on convex compact subsets of Rn and discover how recent developments in translation invariant smooth valuations have led to groundbreaking structures. Understand the significance of two distinct Kahler packages, their relationship through Fourier-type transforms, and their implications for geometric inequalities. Examine how Hodge-Riemann relations connect to the classical Alexandrov-Fenchel inequality for convex bodies, while uncovering new geometric principles through the second structure.