On the SYZ Mirror Symmetry of Log Calabi-Yau Surfaces

DIFFERENTIAL GEOMETRY

Speaker:

Yu-Shen Lin - BU

The Strominger-Yau-Zaslow conjecture predicts the existence of special Lagrangians fibration in Calabi-Yau manifolds near large complex structure limit. The SYZ conjecture has been an important guiding principle for mirror symmetry and many of the implications are verified. In this talk, I will report on the recent progress on the SYZ fibration on certain log Calabi-Yau surfaces using the Lagrangian mean curvature flow and the theory of J-holomorphic curves. As a bi-product, we produce many new special Lagrangian submanifolds. I will also explain the applications in mirror symmetry, including the tropical/holomorphic correspondence for log Calabi-Yau surfaces and a mathematical realization of renormalization process of Hori-Vafa. Part of the talk is based on the joint work with T. Collins, A. Jacob and S-C. Lau, T-J. Lee.