Isomonodromic tau functions from Liouville conformal blocks
Oleg Lisovyy
Lundi 22/09/2014, 11:00
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
I will show 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. In the case n=4 we will thereby express the general solution of Painlevé VI equation in terms of 4-point conformal blocks. Time permitting, I will discuss how the c=1 fusion kernel can be calculated explicitly using this Painlevé/CFT relation.
Contact : Vincent PASQUIER


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