Seminaire du LPTMS: Oleg Lisovyy


11:00 - 12:00

LPTMS, salle 201, 2ème étage, Bât 100, Campus d'Orsay
15 Rue Georges Clemenceau, Orsay, 91405
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Isomonodromic tau functions from Liouville conformal blocks

Oleg Lisovyy, LMPT Université de Tours

I will show that the Riemann-Hilbert problem to find multivalued analytic functions with SL(2,C)-valued monodromy on n-punctured Riemann sphere 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.

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