Young equations in infinite dimension with singularities

In this talk I will present some new results about Young differential equations in infinite dimension with “non smooth” initial datum. During the talk I will introduce the concept of Young integral for non smooth paths defined by Young in 1936 and an algebraic approach to integration with respect to non smooth paths due to Gubinelli in 2004, whose generalization allows to consider abstract Cauchy problems driven by an irregular path. At last, if I will have time, I will give an idea of the of the theory of rough paths started by Terry Lions in 1998 and developed by other authors in the last twenty years.