SISSA Mathematics Colloquium

[Emanuele Tuillier Illingworth]

SISSA MATHEMATICS COLLOQUIUM


O. Lisovyy

Painlevé functions and conformal blocks

Abstract : The sixth Painlevé equation describes monodromy preserving 
deformations of rank 2 Fuchsian systems with four regular singular 
points on the Riemann sphere. The monodromy data play a role of 
integrals of motion for Painlevé VI, and its solution amounts to 
constructing explicit inverse of the Riemann-Hilbert map. We will show 
that this problem can be solved by expressing Painlevé VI tau function 
and the solution of the auxiliary linear system in terms of Fourier 
transforms of Virasoro conformal blocks. We will also discuss various 
generalizations of this isomonodromy/CFT correspondence.

Venue: SISSA, room 136 on Thursday 14 January at 2:30 pm