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Jacques Hurtubise : Isomonodromy deformations of connections

The link between meromorphic connections on a Riemann surface and their monodromy is a very classical one, indeed so classical that it was the subject of one of Hilbert?s problems. The deformation theory of these connections, and when these deformations preserve the monodromy, is almost equally ancient. I will give an overview of some results in the area, some ancient, and some quite recent.

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