Felipe Espreafico (IMJ-PRG): Gauss-Main Connection in Disguise: A «quasi-modularity» for Gromov-Witten invariants for the Quintic Threefold

Gromov-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 Weistrass family of Elliptic Curves. A similar relation may be observed by looking at periods of the mirror quintic family: that 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. This is part of larger program called Gauss-Manin connection in Disguise, that can be also applied in other contexts. We finish by briefly discussing other applications and further questions.

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