Chunlin Shao: What is an almost toric fibration?

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 toric and 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 talk about some operations on ATF and the corresponding operations on the divisors. If time permits, I can talk about the correspondence between ATF and LCY divisors.