Isomonodromic Tau-Functions from Liouville Conformal Blocks

It will be shown that the Riemann-Hilbert problem to find multivalued analytic functions with SL(2,C) -valued monodromy on Riemann surfaces of genus zero with n punctures can be solved by taking suitable linear combinations of the conformal blocks of Liouville theory at c = 1 . This implies a similar representation for the isomonodromic tau-function. The talk is based on the paper arXiv:1401.6104