KASS seminar

Abstract: The formalism of superforms and supercurrents on $\R^n$ is a real variable analog of positive closed forms and currents. It was studied first in the thesis of Aron Lagerberg and has found applications in tropical geometry and the theory of Berkovich spaces. I will discuss its applications to convex geometry, developing the masters thesis of Simon Larsson. The main points are a new proof of the Alexandrov-Fenchel theorem -- mimicking Gromov's proof of the Khovanski-Teissier theorem -- and some tentative applications to Monge-Ampere equations on the boundaries of convex polytopes.