Geometric inequalities for convex sets and valuations theory

Valuations are finitely additive measures on convex sets. The space of translation-invariant valuations carries a number of structures ( i.e., product and convolution), satisfying non-trivial properties. One such recently discovered property is an analogue of the classical Hodge-Riemann relations from algebraic geometry. In special cases, they lead to new inequalities on convex bodies, to be discussed in the talk.
 
No preliminary knowledge of valuation theory or algebraic geometry is necessary to understand the talk.