Yu-Shen Lin : SYZ Mirror Symmetry of Log Calabi-Yau Surfaces

Posted by Philip Engel , part of the Algebraic Geometry Seminar.

At

April 28, 2025, 3 p.m.

In

636 SEO

Abstract

The Strominger-Yau-Zaslow conjecture predicts Calabi-Yau manifolds admit special Lagrangian fibrations and provides a recipe for the mirror construction. In this talk, I will explain the existence of special Lagrangian fibrations in certain log Calabi-Yau surfaces. Moreover, with the suitable mirror map the special Lagrangian fibrations on the mirror pairs are dual to each other. The study of these special Lagrangian fibrations also accidentally proved the Torelli theorems of certain types of gravitational instantons. Moreover, these setup the foundation for the equivalence of certain open Gromov-Witten invariants and log Gromov-Witten invariants.