Online: https://uni-jena-de.zoom.us/j/68512822076
Abstract:
A convex body is a convex, compact subset of n-dimensional Euclidean space. Questions concerning the volume of convex bodies, while often simple to state, can lead to profound and difficult problems, some of which are still open to date. After reviewing some of these problems, we present recent results on valuations on convex bodies which are analogous to the Hodge-Riemann relations in Kähler geometry. We will indicate how these results provide a new perspective on some of the most powerful geometric inequalities for convex bodies known today.
Based on joint work with J. Kotrbaty.
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