Sala Seminari (Dip. Matematica).
We will introduce basic concepts and tools from rough paths theory, motivated by the need to establish a solution theory for differential equations driven by irregular signals. In particular we will discuss controlled rough paths, integration against rough paths, we will compare it to stochastic integration theories and show how classical results can be extended to the rough paths framework. We will mainly consider α-Hölder signals with α∈(1/3,1/2]; this choice allows to simplify many concepts of the theory and, although restrictive, provides enough instruments to deal with interesting problems, like nonlinear SPDEs driven by space-time white noise.