The moduli space ${\cal M}_g^n$ of smooth complex projective curves of genus $g$ equipped with $n$ distinct numbered points is an irreducible algebraic variety of dimension $3g-3+n$ (assuming $n\ge 1$ for $g=1$ and $n\ge 3$ for $g=0$). Its natural compactification $\overline {\cal M}_g^n$ carries line bundles $L_i$, $i=1,\dots n$, defined by “taking the cotangent space at the $i$-th point”. For nonnegative integers $(d_1,d_2,\dots ,d_n)$, let $\langle \tau _{d_1}\tau _{d_2}\cdots \tau _{d_n}\rangle $ be the value of the Chern monomial $c_1(L_1)^{d_1}\dots c_1(L_n)^{d_n}$ on the fundamental of $\overline {\cal M}_g^n$ ($=0$ unless $\sum _i d_i = 3g-3+n$). Witten conjectured that the function $\sum _n {1\over n!}\sum _{d_1,\dots ,d_n} \langle \tau _{d_1}\tau _{d_2}\cdots \tau _{d_n} \rangle T_{2d_1+1}T_{2d_2+1}\dots T_{2d_n+1}$ is modulo a simple rescaling of the logarithm of a $\tau $–function for the K–dV hierarchy. Kontsevich's proof (1991) includes an explicit expansion of this function.