In this course I try to give a self-contained introduction in this field. I want to give an idea what the subject is about, introduce and explain in simple examples the new concepts and mathematical ideas which where developed in that context. Depending on interest, I could also explain in the end some of the relations to string theory and conformal field theory. A detailed overview of the course will be given in the first lecture. Some knowledge in the theory of differential equations.
Examination is by take-home problems.
The course gives 4 points.