In this course I will present an introduction to KAM and Normal form methods for PDEs. The key tools that I shall present are
1) the theory of pseudo-differential operators
2) the reducibility schemes
3) the Nash-Moser theory.
I will present several problems and applications like energy transfer for time dependent Schrödinger equations (growth of Sobolev norms) and (time permitting) construction of quasi-periodic solutions for equations arising from fluid dynamics.
Please see the course schedule at
https://www.gssi.it/education/mathematics-education/academic-calendar-maths-education