Kontsevich-Witten tau-function and the Hodge tau-function
are generating functions for two types of intersection numbers on
moduli spaces of stable curves. Both of them are tau functions for the
KP hierarchy. In this talk, I will describe how to connect these two
tau-functions by differential operators belonging to the
$\widehat{GL(\infty)}$ group. Indeed, these two tau-functions can be
connected using Virasoro operators. This proves a conjecture posted by
Alexandrov. This is a joint work with Gehao Wang.