Abstract "Controlled distributions and applications"
A short course on the basics of the theory of controlled rough paths and recents extensions to a more general class of stochastic objects. We will discuss a series of examples ranging from rough differential equations, some stochastic PDEs and examples of application to the regularization by noise phenomenon for ODEs and PDEs. Most of the topics require very shallow knowledge of stochastic analysis which render the course suitable for non-probabilists too.