Appears in collection : Conférence à la mémoire de Vadim Knizhnik

In the limit of large central charge and large conformal dimensions Virasoro conformal blocks exponentiate, leading to classical conformal blocks. The latter are of much interest, in particular they give solution to the monodromy problem of ordinary linear differential equations with regular singularities. It will be shown how to relate four-point classical conformal blocks to classical action evaluated on special solutions of Painleve VI equation.