PLEASE NOTE:  THIS SEMINAR WILL BE HELD AT COLUMBIA UNIVERSITY IN ROOM MATH 407. The Fukaya category of a Landau-Ginzburg (LG) model W: E --> C, denoted F(E,W), enlarges the Fukaya category of E to include certain non-compact Lagrangians determined by W (for instance, Lefschetz fibrations and their thimbles). I will describe natural functors associated to the Fukaya categories of (E,W) and the general fibre M, and introduce a new Floer homology ring for (E,W). Using these, I will explain two new results: (a) a generation criterion for F(E,W), in the sense of Abouzaid/AFOOO, and (b) exact triangles of functors, one each in F(E,W) and F(M). First applications include stability and generation results for Fukaya categories and a new proof of exact sequences for fibered twists. This is joint work (in preparation) with Mohammed Abouzaid.