On the geometry of isomonodromic differential equations (II)


Masa-Hiko Saito

09:20:00 - 10:20:00

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

In the second talk, I will describe the structure of moduli space of connections in more detail. I will explain about a systematic way to introduce apparent singularities of linear connections which give a half of canonical coordinates $q_i$ of a Zariski open set of the moduli space of connections which is a joint work with S. Szabo. Moreover we will give the dual coordinates $p_i$ to $q_i$, and both of them give a canonical coordinates system of the moduli space, hence the phase space of isomonodromic differential equations. Moreover, we will review our joint work with F. Loray and C. Simpson about the structures of two different Lagrangian fibrations on the moduli spaces, and its relation to the symmetry of Painleve type equations of Okamoto type.

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