Lecture 5 (Thu, Mar 20, 2008)
Riemann–Hilbert Problem: positive results
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Formulation of the problem and its tautological solution on an abstract holomorphic vector bundle
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Meromorhic trivialization and Plemelj theorem (solvability of the problem if one of the monodromies is diagonalizable).
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Invariant subbundles, (ir)reducibility of a regular connexion.
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Lemma on too different orders. Bounds on the splitting type of a bundle with irreducible Fuchsian connexion.
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Bolibruch–Kostov theorem: solvability of the Riemann–Hilbert problem for irreducible representations.
Reading: Sections 18A-18D from the book (printing disabled).
