I have heard that for an ADE singularity $f$, $ D^b\mathrm{Fuk}(f) \simeq D^b(\mathrm{Rep}\ Q)$ where $Q$ is the corresponding Dynkin quiver. (As one would hope, if $\mathrm{Fuk} …

I am trying to understand how all the players in the title relate, but with all the grading shifts,and difficult isomorphisms involved in the subject I am having a hard time being …

Let X be a compact symplectic manifold with a form $\omega$. And $X \times X$ is equipped with the symplectic form $(\omega,-\omega)$. The diagonal $\Delta:X \mapsto X \times X$ is …

So, physicists like to attach a mysterious extra cohomology class in H^2(X;C^*) to a Kahler (or hyperkahler) manifold called a "B-field." The only concrete thing I've seen this B- …

Sometimes people say that the Fukaya category is "not yet defined" in general. What is meant by such a statement? (If it simplifies things, let's just stick with Fukaya categories …

Hi Can one explain to me what is the Hochschild homology of Fukaya category? I mean the definition. You can use the notations of FOOO (Fukaya-Oh-Ono-Ohta) if it helps you to expla …

Good afternoon. Let $M$ be, say, a compact symplectic manifold. Both deformation quantization (as in Kontsevich) and quantum cohomology yield "deformations" (in the appropriate re …

There is a conjecture of Kontsevich which states that Hochschild (co)homology of the Fukaya category of a compact symplectic manifold $X$ is the (co)homology of the manifold. (See …

I just skimmed a bit of this fresh-off-the-press paper on homological mirror symmetry for general type varieties. One thing that intrigued me was statement (ii) of Conjecture 3.3. …

There is an algebraic theory that I'm thinking of trying to develop and I wanted to know if it had any real world prevalence --- I'd like to know an example of a generator L of a F …

At some point in this past year, some Fukaya people I know got very excited about the Fukaya categories of symplectic manifolds with "Lagrangian skeletons." As I understand it, a …

Let X be a compact symplectic manifold. There is an idea, I think probably originally due to Kontsevich, that we should be able to get Gromov-Witten invariants of X out of the Fuka …

I'd really like to hear any references or information people have about the Fukaya categories of hyperkahler reductions of vector spaces (for more informations on the varieties, se …