Speaker: Stephen Pietromonaco (University of British Columbia)

Title: Gromov-Witten Potentials of Local Banana Manifold and Siegel Modular Forms

Abstract: A local banana manifold Y is a Calabi-Yau threefold fibered over a disk by Abelian surfaces such that the singular fiber contains a "banana configuration" of three rational curves. In this talk I will discuss the genus g Gromov-Witten potentials of Y, and show that for g>1 they are Siegel modular forms of weight 2g-2. Moreover, each is produced by a canonical lifting procedure starting with the Eisenstein series of weight 2g. Finally, I will comment on compatibility with predictions from physics and mirror symmetry. This is work with Jim Bryan from 2019, but relevant to new results of Azam-Cannizzo-Lee-Liu.