Venue: Room 204, Hai Na Yuan #2, Zijingang Campus

Time: 16:00 - 17:20, December 15

Speaker: 闵捷 Jie Min(Hetao Institute of Mathematics and Interdisciplinary Sciences)

Pretalk: Introduction to almost toric fibrations

Abstract: In this pretalk, I will cover the basics of toric actions and almost toric fibrations, visible symplectic and Lagrangian submanifolds, blow-up and blow-down operations.

Research talk: Symplectic log Calabi-Yau divisors and almost toric fibrations

Abstract: Lagrangian fibrations sit at the crossroads of integrable systems, toric symplectic geometry and mirror symmetry. A particularly simple and interesting class of Lagrangian fibrations is called almost toric fibrations, whose total spaces are symplectic 4-manifolds. In this talk I will introduce almost toric fibrations over disks and their boundary preimages, which are symplectic divisors representing the first Chern class, called symplectic log Calabi-Yau divisors. I will then talk about joint work with Tian-Jun Li and Shengzhen Ning, showing that given a symplectic log Calabi-Yau divisor, an almost toric fibration can be constructed. I will also outline an application of this construction to understanding Lagrangian spheres in rational surfaces.