Lecture 8 (Thu, Apr 10, 2008)

Geometric and global theory of linear ordinary differential equations

1. Global theory of linear equations. Jet bundles, Cartan distribution. Meromorphic connexion associated with a linear equation.
2. “Natural bundle” for a globally Fuchsian equation. Sum of characteristic exponents.
3. Riemann–Hilbert problem for Fuchsian equations. Hypergeometric equation.