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Isomonodromic tau functions from Liouville conformal blocks

Le : 20/02/2014 16h30
Par : Oleg LISOVYY (Université de Tours)
Lieu : I 103
Lien web :
Résumé : I will show that 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.