中科院数学与系统科学研究院
数学研究所
中科院华罗庚数学重点实验室
华罗庚青年数学论坛
综合报告
报告人： 袁航 博士（Northwestern University）
题 目：A mathematically precise version of SYZ conjecture and examples
时 间：2023.06.30（星期五），15:00-16:00
地 点：数学院南楼N913
摘 要：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 An singularities. These examples are consistent with all known mirror symmetry results, offering strong support for the SYZ T-duality principle.
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