The Airy, Sine and Pearcey processes have come up as limiting processes in Brownian motion , random matrix theory and also random growth processes.The Airy and Sine processes involve respectively the limiting process, properly scaled, for the largest and middle eigenvalue in the Dyson process for the spectrum of $n \times n$ Hermitian matrices,as $n$ gets large.The Pearcey process involves on the one hand $2n$-noncolliding Brownian motions conditioned to emanate from $x=0$ at $t=0$, with half to end at $n^{\frac{1}{2}}$ and the other half to end at $-n^{\frac{1}{2}}$ at $t=1$, and one looks with a microscope at what at happens at $t=\frac{1}{2}$ as the 2 groups finally start separating, as $n$ gets large.This is equivalent to an $n \times n$ random Hermitian matrix problem with a specific magnetic potential, as the spectrum starts splitting into 2 groups, as $n$ gets large.We get p.d.e.’s for the basic statistics of these problems using integrable $\tau$-function theory and Virasoro methods.