  We establish the relation between two objects: an integrable system related
to Painleve II equation, and the symplectic invariants of a certain plane curve
\Sigma_{TW} describing the average eigenvalue density of a random hermitian
matrix spectrum near a hard edge (a bound for its maximal eigenvalue). This
explains directly how the Tracy-Widow law F_{GUE}, governing the distribution
of the maximal eigenvalue in hermitian random matrices, can also be recovered
from symplectic invariants.
