Mathematics Colloquia and Seminars

Return to Colloquia & Seminar listing

We consider Legendrian surfaces in complex three-space described by cubic planar graphs, and the moduli space of spacetime-filling Lagrangian D-branes with asymptotics defined by the Legendrian surfaces. The superpotential in four dimensions is determined by open disk Gromov-Witten invariants, i.e. holomorphic disks mapping to complex three-space whose boundary maps to the Lagrangian. Following Aganagic-Vafa and Aganagic-Klemm-Vafa, we determine the superpotential by expressing the moduli space as the graph of its differential. The same moduli space has appeared in the work of Dimofte-Gabella-Goncharov, who consider three-dimensional compactifications and their partition functions.

We show that the all-genus open Gromov-Witten invariants of all such Lagrangians can be determined by cluster theory from a particularly simple initial seed. I will try to focus on describing how one performs the necessary computations.

This talk is based on joint work with David Treumann and Linhui Shen.

bring lunch!