Sala Seminari (Dip. Matematica).
We present how the problem of coarea formula in the Heisenberg group leads us rather unexpectedly to a system of “level set differential equations”, generated by a defining mapping of very low regularity. In this system we cannot write classical derivatives, since its formally associated vector field does not exist a priori. We solve this problem using tools from rough path theory, where a privileged role is played by the sewing lemma. These results have been obtained in collaboration with Dario Trevisan and Eugene Stepanov.