Integrals of $\psi$-classes over double ramification cycles

Double ramification cycles are certain codimension $g$ cycles in the moduli space $\overline{\mathcal M}_{g,n}$ of stable genus $g$ curves with $n$ marked points. They have proved to be very useful in the study of the intersection theory of $\overline{\mathcal M}_{g,n}$. In my talk I will explain that integrals of arbitrary monomials in $\psi$-classes over double ramification cycles have an elegant expression in terms of vacuum expectations of certain operators that act in the infinite wedge space.
The talk is based on a joint work with S. Shadrin, L. Spitz and D. Zvonkine.