I will discuss some recent results concerning the extension of the Young integral in arbitrary dimension and codimension. We will work within the setting of charges, and give examples thereof: charges measuring the increments of some mutiparameter stochastic processes (among them the fractional Brownian sheet), and the Hölder differential forms that appear in an integral of R. Züst.

The talk is partially based on joint work with T. De Pauw. See https://arxiv.org/abs/2401.15427 https://arxiv.org/abs/2401.15423 and https://arxiv.org/abs/2403.17600