Abstract: In this talk I will start by reviewing some results of Okounkov-Pandharipande and Bloch-Okounkov on the generating series of Gromov-Witten invariants of elliptic curves. I will then report my recent results on this topic.  These include period integral formulas for the (all genus) n-point functions, and new combinatorial formulas of them.

The talk is based on my works arXiv:2304.03912 and arXiv:2310.08018.