The generating series of Gromov-Witten invariants of an elliptic orbifold curve are known
to be quasi-modular forms basing on the fact that the WDVV systems satisfied by them are equivalent to
the Ramanujan identities for the corresponding quasi-modular forms. In this talk I will explain how the
local expansions of these quasi-modular forms near the elliptic fixed point on the upper-half plane yield the
generating series in a completely different enumerative theory, the FJRW theory. This on the one hand gives
the correspondence between the Gromov-Witten theory and FJRW theory for the elliptic orbifold curves,
on the other hand provides geometric contexts in which the local expansions of certain quasi-modular forms
carry interesting enumerative meanings.
The talk is based on a joint work with Y. Shen.