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In this letter,we present our conjecture on the connection between theKontsevich--Witten and the Hurwitz tau-functions. The conjectural formulaconnects these two tau-functions by means of the $GL(\infty)$ group element. Animportant feature of this group element is its simplicity: this is a groupelement of the Virasoro subalgebra of $gl(\infty)$. If proved, this conjecturewould allow to derive the Virasoro constraints for the Hurwitz tau-function,which remain unknown in spite of existence of several matrix modelrepresentations, as well as to give an integrable operator description of theKontsevich--Witten tau-function.

From Hurwitz numbers to Kontsevich-Witten tau-function: a connection by Virasoro operators