A Mathematically Precise Version of SYZ Conjecture and Examples
Time: 2023-07-07
Published By: Wenqiong Li
Speaker(s): Hang Yuan (Northwestern University)
Time: 15:00-16:00 July 10, 2023
Venue: Room 29, Quan Zhai, BICMR
We discuss the Strominger-Yau-Zaslow (SYZ) conjecture, which provides a geometric framework to understand mirror symmetry. We emphasize the challenges in precisely formulating the conjecture. We propose a straightforward local SYZ fibration duality between two types of integrable systems found in Kahler and Berkovich geometry. Then, the global SYZ fibration duality takes the shape of this local schema but with a nontrivial gluing process that relies on the singular Lagrangian fibers and quantum correction data. We also explain how the non-archimedean topology can be utilized to incorporate singular dual fibers. Time permitting, we conclude with explicit examples, such as conifold and $A_n$-singularities. These examples are consistent with all known mirror symmetry results, offering strong support for the SYZ T-duality principle.
