The objective of this research in pair is to advance in the study of (stochastic)
partial differential equations and “rough” evolution equations within the framework of the theory of rough paths, using tools from functional analysis such as the Trotter-Kato formula, etc. If the theory of rough paths has been proved to be successful to deal with evolution equations with bounded operators, its transposition to unbounded operators presents some serious issues. A possible application to the stochastic Schrödinger equations, to circumvent the lack of regularization in mild solutions, will be considered.