Aron Lagerberg: Positive super currents and tropical geometry in R^n

In this talk, we will introduce the formalism of positive super currents on R^n, in strong analogy with positive currents in the complex setting. We can transfer notions from the complex theory, such as Lelong numbers and intersection of currents, into this real setting. As an application, we show that these super currents provide a framework for tropical geometry in R^n. More precisely, we can identify a tropical hypersurface with a positive super current, in analogy with the correspondence between a complex variety and its current of integration.