| Résume | Gromov-Witten invariants and modularity are topics that often come together. In this talk, we will explore a type of modularity for the genus zero invariants for the quintic threefold, focusing on open invariants. By looking at periods of the mirror quintic family, we show
that generating functions for instanton numbers can be written in terms of solutions to certain differential systems coming from the Gauss-Manin connection that generalize the classical Ramanujan equations that give rise to Eisenstein series. This is part of larger program called Gauss-Manin connection in Disguise, that can be also applied in other contexts. We finish by briefly discussing other applications and further questions.
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