Let me do some concrete stuff tonight.

• Write up and finish the complete intersection project.
• write up the legendrian thickening stuff
• write up the matrix factorization for conifold case. who goes to what.
• dream about, how to do A-side GIT quotient.

So far, what do I know? If I choose a character on the B-side, that means I choose a cocharacter on the A-side. It can mean a weight shifting functor $S$.

We first need to look at the equivariant object $F$, then among those, we need to look at how $F$ maps to $SF$.

We can say $Fuk(Y, W_Y)$ is mirror to $Coh(X, W_X)$. We have $T$ acts on $X$ preserving $W_Y$, and $Y$ maps to $T^\vee$ (how does this map interact with $W_Y$ ?).