Density of stationary geodesic nets and parametric isoperimetric inequalities

Certain parametric versions of the classical isoperimetric and coarea inequalities turn out to be closely related to problems in Almgren-Pitts Min-Max theory. I will describe some results from an ongoing work with Larry Guth on parametric inequalities and the Weyl for volume spectrum in higher codimension, as well as a joint work with Bruno Staffa on density of stationary geodesic nets in Riemannian manifolds.