A Mathematically Precise Version of SYZ Conjecture and Examples
发布时间：2023年07月07日
浏览次数：1335
发布者: Wenqiong Li
主讲人： 袁航（西北大学）
活动时间： 从 2023-07-10 15:00 到 16:00
场地： 北京国际数学研究中心，全斋全29教室
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.
