Almgren's isomorphism theorem and parametric isoperimetric inequalities

In the 60's Almgren initiated a program for developing Morse theory on the space of flat cycles. I will discuss some simplifications, generalizations and quantitative versions of Almgren's results about the topology of the space of flat cycles and their applications to minimal surfaces.

I will talk about joint works with F. C. Marques and A. Neves, and L. Guth.