I was discussing with Yixuan yesterday. He mentioned a few works by Siu-Cheong Lau are noteworthy.

• Localized mirror functor. No, not just probing the space using a compact immersed Lagrangian, but with deformation, allowing immersed Lagrangians.
• Nakajima quiver variety coming from Floer theory

Then, I am also going to meet with Denis Auroux. His not-so-recent work with Abouzaid is about fibered Lagrangian. There is one thing that is quite interesting to me: consider the very singular fibration $f: \C^3 \to \C$, $f=xyz$. Consider a Lagrangian, say living over the line $Re f = -1$, and in the fiber, we pick the 'positive real' slice in $(\C^*)^2$. I am not sure what does 'positive real mean, but it must be cocore to the compact Lagrangian, which I think is well-defiend $|x|=|y|=|z|$ in each fiber. OK, great, then turn on the gradient flow for $Re(f)$, do we get a nice thim