Abstract: Given a holomorphic curve in the complex 2-plane together
with a suitably normalized symmetric meromorphic bilinear
differential, the Chekhov-Eynard-Orantin Topological Recursion defines
an infinite sequence of symmetric meromorphic multilinear
differentials W_{g,n} on the curve. In many examples, the invariants
W_{g,n} provide answers to enumerative problems. I will describe
Topological Recursion and present several examples in which the
answers are Hodge integrals (which are intersection numbers on moduli
of curves) or Gromov-Witten invariants (which are virtual counts of
holomorphic maps from Riemann surfaces to a Kähler manifold).