Painlevé equations are nonlinear 2nd order ordinary differential equations (ODEs) which describe monodromy preserving deformations of linear ODEs. Their solutions can be seen as nonlinear counterparts of the classical special functions of hypergeometric type such as Airy, Bessel, etc. We will describe a correspondence between the isomonodromy theory and 2D CFT which relates Painlevé functions and conformal blocks of the Virasoro algebra.
