Isomonodromic tau functions from Liouville conformal blocks (I)


Oleg Lisovyi

16:10:00 - 17:10:00

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

I will explain how the Riemann-Hilbert problem associated to isomonodromic deformations of rank $2$ linear systems with $n$ regular singular points on $mathbb{P}^1$ can be solved by taking suitable linear combinations of conformal blocks of the Virasoro algebra at $c=1$. This implies a similar representation for the isomonodromic tau function. In the case $n=4$, it provides the general solution of the Painlev'e VI equation in the form of combinatorial sum over pairs of Young diagrams.

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