Gauss-Manin Connection in Disguise: A «quasi-modularity» for Gromov-Witten invariants for the Quintic Threefold

Speakers: Felipe Espreafico Guelerman (Jussieu)\n\nGromov-Witten invariants and modularity are topics that often come together. In this talk, we will explore a type of quasi-modularity for the genus zero invariants for the quintic threefold. We start by explaining how classical Eisenstein series are related to periods of the Weiestrass family of Elliptic Curves. Then, we will show a similar relation by looking at periods of the mirror quintic family: generating functions for the genus zero invariants can be written in terms of solutions to certain differential systems coming from the Gauss-Manin connection that generalize the classical Ramanujan equations that give rise to Eisenstein series. Building on the work of Walcher and Alim-Lange, we explain how higher genus invariants can also be expressed in terms of this ‘generalizations of Eisenstein series’.\n\nhttps://indico.math.cnrs.fr/event/16100/