Focused Workshop on Current Trends in Geometric Valuation Theory

Geometric valuation theory has a long history, extending from Dehn's solution of Hilbert's third problem to modern advances in discrete geometry, integral geometry, and asymptotic geometric analysis. Much recent attention has focused on the algebraic structure of smooth valuations on convex bodies, leading to results such as the hard Lefschetz theorem and Hodge–Riemann relations, and, consequently, to new geometric inequalities. An important parallel development has been the extension of valuations to convex functions, including a Hadwiger-type classification result and a theory of smooth valuations. This workshop will bring together experts from both of these areas, in order to foster collaboration and explore new connections between the algebraic structure of smooth valuations on convex bodies and the theory of valuations on convex functions.