Gromov-Witten invariants of elliptic curves revisited

• 主讲人：Jie Zhou (Yau Mathematical Sciences Center, Tsinghua University)
• 举办方： Beijing-Saint Petersburg Mathematics Colloquium
• 时间： 2025-06-05 20:00 - 2025-06-05 21:00
• 地点： Online

​

To Join Tencent Meeting: https://meeting.tencent.com/dm/LisB1icKvvyu

Meeting ID: 927-4841-9441    Password: 202503

 

Abstract: Elliptic curves play an important role in understanding the modern aspects of enumerative geometry. 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 from the perspective of the mirror elliptic curve. These include:

1. a formulation of the (all-genus) generating series as period integrals on the configuration space of the mirror curve,

2. new combinatorial formulas for the generating series,

3. a connection between a slightly modified but equivalent version of the generating series and mixed Hodge structures on the cohomology of configuration spaces of the mirror curve.

The talk is based on my recent works arXiv:2304.03912, arXiv:2310.08018, arXiv:2305.12362.

 

Bio: Jie Zhou is an associate professor at the Yau Mathematical Sciences Center of Tsinghua University. He obtained his PhD degree from Harvard University in 2014 and did postdoctoral researchers at Perimeter Institute in Canada and University of Cologne in Germany, before joining Tsinghua University in 2018. His research interest lies at the intersection of enumerative geometry, mirror symmetry, and modular forms.