Talks

On the geometry of isomonodromic differential equations (I)

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Masa-Hiko Saito

2014-03-22
11:00:00 - 12:00:00

308 , Mathematics Research Center Building (ori. New Math. Bldg.)



In the first talk, I will review on our joint work on the geometry of isomonodromic differential equations of Inaba-Iwasaki-Saito and Inaba-Saito. First we review on the work for the algebraic construction of the moduli space of linear connections on a smooth projective curve with fixed formal types of regular or unramified irregular singularities. Moreover we can construct the moduli spaces of monodromy data including the monodromy data, Stokes data. Then we can define the generalized Riemann-Hilbert correspondences between the moduli space of linear connections (differential equations) and the moduli of generalized monodromy data as an analytic morphism. Then under the mild technical conditions, we can show that the Riemann-Hilbert correspondences are analytic isomorphisms, which give a complete proof of geometric Painleve property of the isomonodromic differential equations whose phase space can be identified with the moduli spaces of linear connections.

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