# A criterion for generating Fukaya categories of fibrations

 Princeton/IAS Symplectic Geometry Seminar Topic: A criterion for generating Fukaya categories of fibrations Speaker: Sheel Ganatra Affiliation: Stanford University Date: Friday, February 21 Time/Room: 1:30pm - 2:30pm/S-101 Video Link: https://video.ias.edu/pisgs/2014/0221-SheelGanatra

The Fukaya category of a fibration with singularities $W: M \to C$, or Fukaya-Seidel category, enlarges the Fukaya category of $M$ by including certain non-compact Lagrangians and asymmetric perturbations at infinity involving $W$; objects include Lefschetz thimbles if $W$ is a Lefschetz fibration. I will recall this category and then explain a criterion, in the spirit of work of Abouzaid and Abouzaid-Fukaya-Oh-Ohta-Ono, for when a finite collection of Lagrangians split-generates such a fibration. The new ingredients needed include a Floer homology group associated to $(M,W)$ and the Serre functor. This is work in progress with Mohammed Abouzaid.