Gromov-Witten theory and cycle-valued modular forms

Gromov-Witten theory and cycle-valued modular forms

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Yefeng Shen , University of Michigan
Fine Hall 401

A remarkable phenomenon in Gromov-Witten theory is the appearance of (quasi)-modular forms. For example, Gromov-Witten generating functions for elliptic curve, local $\mathbb{P}^2$, elliptic orbifold $\mathbb{P}^1$ are all (quasi)-modular forms. In this talk, we will discuss modularity property of the Gwomov-Witten cycles of elliptic orbifold $\mathbb{P}^1$. Since Gromov-Witten cycles live in the cohomology space of moduli of pointed curves, our result gives a geometric realization of a collection of vector-valued (quasi)-modularity forms via Gromov-Witten theory. This work is joint with Todor Milanov and Yongbin Ruan.