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I am studying the isomonodromic deformations theory, which leads in the case of a $\mathcal{C}_{0,4}$ Riemann surface to the sixth Painlevé equation.

I read that this equation had a $\tau$-structure, so we can determine a $\tau$ function associated to isomonodromic deformations.

Here is my silly question : what is a $\tau$-structure, why is it important ?

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    $\begingroup$ I don't even know what a $\tau$ function means! there seems to be connections with symplectic geometry or hamiltonian formulation in physics, but it's quite mysterious to me. $\endgroup$ – Julien Roussillon Jun 29 '15 at 8:20

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