The mini-course of 9 lectures on differential equations with regular singularities. The themes covered include: Definition of connection and differential equation. Local theory of meromorphic connections with regular singularities. Global theory. Hilbert's 21st problem ( Riemann-Hilbert's problem ), Birkhoff-Grothendieck theorem, Birkhoff standard forms. The course is elementary and will cover some of the material already explained at the Fourier seminar last year. It is aimed at physicists, math students and anybody who missed some of the Fourier seminars and would like to catch up. We loosely follow Bolibrukh's course with the same name, lectures 1-12 in his book "Inverse monodromy problems in analytic theory of differential equations"
The schedule is as follows (click for the lecture notes).
10:30-12:00 - Lecture 1: Introduction (Todor Milanov)
13:30-15:00 - Lecture 2: Local theory I (Alexander Getmanenko)
16:00-17:30 - Lecture 3: Local theory II (Sergey Galkin)
10:30-12:00 - Lecture 4: Local theory III (Todor) +exercises
16:00-17:30 - Lecture 5: Global theory (Sergey)
10:30-12:00 - Lecture 6: Riemann-Hilbert's problem (Sasha)
10:30-12:00 - Lecture 7: Birkhoff-Grothendieck's theorem and its corollaries (Todor)
13:30-15:00 - Lecture 8: Another proof of Riemann-Hilbert (Sasha)
16:00-17:30 - Lecture 8.5: Counter-example to Riemann-Hilbert (Sergey)
17:30-18:00 - Lecture 9: Birkhoff standard forms (Sergey)
19:00 afterword, discussion