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Mirror symmetry and elliptic curves. (English) Zbl 0913.14007
Dijkgraaf, R. H. (ed.) et al., The moduli space of curves. Proceedings of the conference held on Texel Island, Netherlands, during the last week of April 1994. Basel: Birkhäuser. Prog. Math. 129, 149-163 (1995).
Summary: The author reviews how recent results in quantum field theory confirm two general predictions of the mirror symmetry program in the special case of elliptic curves: (1) counting functions of holomorphic curves on a Calabi-Yau space (Gromov-Witten invariants) are ‘quasi-modular forms’ for the mirror family; (2) they can be computed by a summation over trivalent Feynman graphs.
For the entire collection see [Zbl 0827.00037].

14H52 Elliptic curves
14J32 Calabi-Yau manifolds (algebro-geometric aspects)
11G05 Elliptic curves over global fields