Speaker:  Sebastian Haney (Columbia University)

Title: Open enumerative mirror symmetry for lines in the mirror quintic

Abstract: One of the early achievements of mirror symmetry was the prediction of genus zero Gromov-Witten invariants for the quintic threefold in terms of period integrals on the mirror. Analogous predictions for open Gromov-Witten invariants in closed Calabi-Yau threefolds can be formulated in terms of relative period integrals on the mirror, which govern extensions of variations of Hodge structure. I will discuss work in preparation in which I construct an immersed Lagrangian in the quintic and show that it supports a family of objects in the Fukaya category mirror to vector bundles on lines in the mirror quintic. The open Gromov-Witten invariants of this Lagrangian are irrational, and can be computed from homological mirror symmetry.