The goal of these notes is to give a short introduction to Fukaya categories and some of their
applications. The first half of the text is devoted to a brief review of Lagrangian Floer (co) …

This paper is about the Fukaya category of a Fano hypersurface X⊂ CP n X⊂CP^n.
Because these symplectic manifolds are monotone, both the analysis and the algebra …

Let. M; J; g;/be a Calabi–Yau m-fold, and consider compact, graded Lagrangians L in M.
Thomas and Yau [81, 82] conjectured that there should be a notion of 'stability'for such L …

We prove that the wrapped Fukaya category of a punctured sphere ($ S^{2} $ with an
arbitrary number of points removed) is equivalent to the triangulated category of singularities …

This review of the theory of toric Landau–Ginzburg models describes an effective approach
to mirror symmetry for Fano varieties. It focuses mainly on the cases of dimensions $2 $ and …

We prove a general form of the wall-crossing formula which relates the disk potentials of
monotone Lagrangian submanifolds with their Floer-theoretic behaviour away from a …

This paper realises the Khovanov homology of a link in $ S^ 3$ as a Lagrangian Floer
cohomology group, establishing a conjecture of Seidel and the second author. The starting …

The $ n $-dimensional pair of pants is defined to be the complement of $ n+ 2$ generic
hyperplanes in $\mathbb {CP} n $. We construct an immersed Lagrangian sphere in the pair …

We show that the category of coherent sheaves on the toric boundary divisor of a smooth
quasi-projective toric DM stack is equivalent to the wrapped Fukaya category of a …

We construct geometric maps from the cyclic homology groups of the (compact or wrapped)
Fukaya category to the corresponding $ S^ 1$-equivariant (Floer/quantum or symplectic) …