Time: Tuesday, 12h-14h,
Room: SR 210 Arnimallee 3
Galois theory relates questions about algebraic extensions of fields to (finite) Galois groups. Differential Galois theory relates questions about linear differential equations to (algebraic) differential Galois groups. Galois theory takes place in a more general context of algebra (rings, modules, fields, etc.); differential Galois theory takes place in the context of differential algebra.
The first goal of this seminar is to learn the basics of differential algebra and its application to differential Galois theory. The second goal is to connect differential Galois theory to the analytic theory of linear differential equations of complex functions in one variable, and to explain the classical Riemann-Hilbert correspondence in the case of the complex plane.
We will follow parts of the textbook
- Galois theory of linear differential equations (Springer Grundlehren der mathematischen Wissenschaften), Singer and Van der Put.
Another good introduction to the subject is the following paper:
- A first look at differential algebra, Hubbard and Littell
The program for the first eight talks is written. The rest of the talks will be adapted to the interests of the participants.