Steiner tree problem revisited through rectifiable G-currents

Steiner tree problem consists in finding a connected set of minimal 1-dimensional measure containing a (prescribed) finite set of points in R^n. I will show how to understand this as a mass minimization problem in a family of currents with coefficients in a suitable group. This allows to introduce calibrations in this problem and therefore to prove the absolute minimality of some concrete configurations. No previous knowledge by the audience in geometric measure theory will be assumed.

This is joint work with Annalisa Massaccesi.