Generating functions for Gromov-Witten invariants and their modular and holomorphic properties SÉMINAIRE ANNULÉ À CAUSE DES GRÈVES

For the Calabi-Yau 3-fold case we review the definition of
the generating functions for open and closed Gromov-Witten invariants,
their r^ole in mirrror symmetry and their relation to physical BPS
states. We explain the techniques by which these functions can be
determined on non-compact and compact Calabi-Yau spaces. Here we focus
on the holomorphic anomaly equations and the matrix model approach and
give explicite examples of their expansions at various interesting
points in the moduli space.