Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces

10/07/2022 9:30 am - 10:30 am
Charles Doran Mauricio Romo Tsung-Ju Lee
CMSA Room G10
Address: CMSA, 20 Garden Street, Cambridge, MA 02138 USA

Algebraic Geometry in String Theory Seminar

Speaker: Sam Bardwell-Evans, Boston University
Title: Scattering Diagrams from Holomorphic Discs in Log Calabi-Yau Surfaces
Abstract: In this talk, we construct special Lagrangian fibrations for log Calabi-Yau surfaces and scattering diagrams from Lagrangian Floer theory of the fibers. These scattering diagrams recover the algebro-geometric scattering diagrams of Gross-Pandharipande-Siebert and Gross-Hacking-Keel. The argument relies on a holomorphic/tropical disc correspondence to control the behavior of holomorphic discs, allowing us to relate open Gromov-Witten invariants to log Gromov-Witten invariants. This talk is based on joint work with Man-Wai Mandy Cheung, Hansol Hong, and Yu-Shen Lin.