Conformal field theory of Painlevé VI

Generic Painlevé VI tau function τ ( t) can be interpreted as four-point correlator of primary fields of arbitrary dimensions in 2D CFT with c = 1. Using AGT combinatorial representation of conformal blocks and determining the corresponding structure constants, we obtain full and completely explicit expansion of τ ( t) near the singular points. After a check of this expansion, we discuss examples of conformal blocks arising from Riccati, Picard, Chazy and algebraic solutions of Painlevé VI.