Georgia Institute of Technology College of Sciences

Valuations are finitely additive measures on convex compact sets. In the last two decades a number of structures (e.g. product and convolution)  with non-trivial properties were discovered on the space of valuations. One such recently discovered property is an analogue of the classical Hodge-Riemann bilinear relations known in algebraic/Kaehler geometry. In special cases, they lead to new inequalities for convex bodies, to be discussed in the talk. No familiarity with valuations theory and algebraic/Kaehler geometry is assumed.