中央研究院數學研究所

Special Colloquium

Special Lagrangian submanifolds in collapsing Calabi-Yau manifolds

2025/12/04 (Thu.) 15:30~16:30

Date : 2025/12/04 (Thu.) 15:30~16:30
Location : Seminar Room 638, Institute of Mathematics (NTU Campus)
Speaker : Shih-Kai Chiu (University of California, Irvine)
Abstract : Special Lagrangian submanifolds play an important role in recent developments of symplectic geometry, minimal surface theory, and SYZ mirror symmetry, and counting them are expected to produce enumerative invariants of Calabi–Yau manifolds analogous to those arising in four-dimensional Yang–Mills theory. However, interesting examples remain scarce, particularly in these contexts. In this talk, I will describe new analytic gluing constructions of special Lagrangians in collapsing Calabi–Yau manifolds, where the ambient Calabi–Yau manifolds admit a fibration structure and the special Lagrangians arise from certain types of graphs in the base. Unsurprisingly, the geometry of (singular) Kähler–Einstein metrics plays a crucial role in these constructions.