In this paper, we present an explicit formula that connects the Kontsevich-Witten tau-function and the Hodge tau-function by differential operators belonging to the $hat{GL(infty)}$ group. Indeed, we show that the two tau-functions can be connected using Virasoro operators. This proves a conjecture posted by Alexandrov in [1].
We describe a new algorithm for computing braid orbits on Nielsen classes. As an application we classify all families of affine genus zero systems; that is all families of coverings of the Riemann sphere by itself such that the monodromy group is a primitive affine permutation group.
