  In [5] I.P. Goulden, D.M. Jackson, and R. Vakil formulated a conjecture
relating certain Hurwitz numbers (enumerating ramified coverings of the sphere)
to the intersection theory on a conjectural Picard variety. We are going to use
their formula to study the intersection theory on this variety (if it is ever
to be constructed) by methods close to those of M. Kazarian and S. Lando in
[7]. In particular, we prove a Witten-Kontsevich-type theorem relating the
intersection theory and integrable hierarchies.
  We also extend the results of [7] to include the Hodge integrals over the
moduli spaces, involving one lambda-class.
